<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@c5fe70257f0f4fc782a97751d3d77f34" data-block-type="vertical" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="False" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Problem 1</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_5a6278f828bb4fea87b0fdea1a6d96c0" class="problems-wrapper" role="group" aria-labelledby="5a6278f828bb4fea87b0fdea1a6d96c0-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART A &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@5a6278f828bb4fea87b0fdea1a6d96c0-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;A school wants to illuminate six corridors, labeled A, B, C, D, E and F. The corridors are portrayed in Figure 1. Each corridor can be illuminated by placing lights at one or both ends of the corridor, which we label as intersections 1 to 5. The luminosity required for each corridor is given in Table 1. For example, the luminosity in Corridor A is required to be 250. This requirement should be interpreted as meaning that the sum of the luminosities of bulbs at Intersections 1 and 2 must be at least 250. Remember that one cannot place bulbs at an intersection unless one first puts in a lighting fixture.&lt;/p&gt; &lt;p&gt;The cost of placing the light fixtures is $450 per corner. (There is no cost if there is no light fixture in a corner.) The cost of the bulbs is $2 per luminosity unit. The maximum luminosity that can be placed in any light fixture is 300 units. The number of units of luminosity is permitted to be fractional. As an illustration, to create a luminosity of 60.5 at a corner with a light fixture requires an expense of $121 in bulbs plus an expense of $450 for putting in the light fixture. &lt;/p&gt; &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/f185a2e26cb9f2a982549313053ca1ef/asset-v1:MITx+15.053x+3T2016+type@asset+block/corridor.png&#34;&gt; &lt;img width=&#34;826&#34; height=&#34;637&#34; alt=&#34;corridor&#34; src=&#34;/assets/courseware/v1/f185a2e26cb9f2a982549313053ca1ef/asset-v1:MITx+15.053x+3T2016+type@asset+block/corridor.png&#34;/&gt; &lt;/a&gt; &lt;p&gt;Formulate this problem as a mixed integer linear program in which the objective is to minimize the cost. For this first formulation, the decision variables should be represented as follows:&lt;/p&gt; &lt;ul&gt; &lt;li&gt;\(y_i\) equals 1 if we place a light fixture in intersection \(i\); 0, otherwise. \(i \in \{1,\ldots,5 \}\)&lt;/li&gt; &lt;li&gt;\(x_i\) the luminosity units of light bulb(s) in intersection \(i. i \in \{1,\ldots,5 \}\)&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;Choose the correct objective function from below&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; id=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0_2_1-choice_0-label&#34; for=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; MIN \(2 \sum_{i=1}^5 y_i + 450 \sum_{i=1}^5 x_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; id=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0_2_1-choice_1-label&#34; for=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; MIN \(250 \sum_{i=1}^5 y_i + \sum_{i=1}^5 x_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; id=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0_2_1-choice_2-label&#34; for=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; MIN \(1250 \sum_{i=1}^5 y_i - 2 \sum_{i=1}^5 x_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; id=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0_2_1-choice_3-label&#34; for=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; MIN \(450 \sum_{i=1}^5 y_i - \sum_{i=1}^5 x_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; id=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;5a6278f828bb4fea87b0fdea1a6d96c0_2_1-choice_4-label&#34; for=&#34;input_5a6278f828bb4fea87b0fdea1a6d96c0_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;&gt; MIN \(450 \sum_{i=1}^5 y_i + 2 \sum_{i=1}^5 x_i\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_5a6278f828bb4fea87b0fdea1a6d96c0_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_5a6278f828bb4fea87b0fdea1a6d96c0_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART A&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_5a6278f828bb4fea87b0fdea1a6d96c0&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_5a6278f828bb4fea87b0fdea1a6d96c0&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;5a6278f828bb4fea87b0fdea1a6d96c0-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;5a6278f828bb4fea87b0fdea1a6d96c0-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;5a6278f828bb4fea87b0fdea1a6d96c0-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_7c9a9a07820e49989fc182eb6627bcb4" class="problems-wrapper" role="group" aria-labelledby="7c9a9a07820e49989fc182eb6627bcb4-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;7c9a9a07820e49989fc182eb6627bcb4-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART B &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@7c9a9a07820e49989fc182eb6627bcb4-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Below is a partial formulation. Which of the following constraints should be added to the formulation to make it correct?&lt;/p&gt; &lt;span&gt; &lt;p class=&#34;equation&#34;&gt;\(\left. \begin{array}{rrcl} &amp;amp; \min &amp;amp; 450 \sum_{i=1}^5 y_i + 2 \sum_{i=1}^5 x_i &amp;amp; &amp;amp; \\ \text {s.t.:} &amp;amp; &amp;amp; &amp;amp; \\ (1)&amp;amp; x_1 + x_2 &amp;amp; \ge &amp;amp; 250 \\ (2)&amp;amp; x_1 + x_3 &amp;amp; \ge &amp;amp; 300 \\ (3)&amp;amp; x_2 + x_3 &amp;amp; \ge &amp;amp; 150 \\ (4)&amp;amp; x_2 + x_4 &amp;amp; \ge &amp;amp; 200 \\ (5)&amp;amp; x_3 + x_5 &amp;amp; \ge &amp;amp; 350 \\ (6)&amp;amp; x_4 + x_5 &amp;amp; \ge &amp;amp; 180 \\ (7)&amp;amp; y_i \in \{0,1 \}, &amp;amp;\forall i \in \{1, \ldots, 5 \} \\ (8)&amp;amp; x_i \geq 0, &amp;amp; \forall i \in \{1, \ldots, 5 \} \\ \end{array}\right\}\)&lt;/p&gt; &lt;/span&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34; id=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;7c9a9a07820e49989fc182eb6627bcb4_2_1-choice_0-label&#34; for=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;&gt; \(x_i \leq 300 y_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34; id=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;7c9a9a07820e49989fc182eb6627bcb4_2_1-choice_1-label&#34; for=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;&gt; \(x_i \geq 300 y_i\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34; id=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;7c9a9a07820e49989fc182eb6627bcb4_2_1-choice_2-label&#34; for=&#34;input_7c9a9a07820e49989fc182eb6627bcb4_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;&gt; Neither i nor ii &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_7c9a9a07820e49989fc182eb6627bcb4_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_7c9a9a07820e49989fc182eb6627bcb4_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART B&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_7c9a9a07820e49989fc182eb6627bcb4&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_7c9a9a07820e49989fc182eb6627bcb4&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;7c9a9a07820e49989fc182eb6627bcb4-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;7c9a9a07820e49989fc182eb6627bcb4-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;7c9a9a07820e49989fc182eb6627bcb4-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_972e5a4378c8481ba0572b8b96b21dca" class="problems-wrapper" role="group" aria-labelledby="972e5a4378c8481ba0572b8b96b21dca-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;972e5a4378c8481ba0572b8b96b21dca-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART C &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@972e5a4378c8481ba0572b8b96b21dca-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Solve the cost-minimization problem you formulated using Julia/JuMP or Excel. What is the total cost you get under the optimal solution (rounded to the nearest whole number)? Error checking hint: the answer is between 2800 and 2819.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; id=&#34;input_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; data-input-id=&#34;972e5a4378c8481ba0572b8b96b21dca_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_972e5a4378c8481ba0572b8b96b21dca_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_972e5a4378c8481ba0572b8b96b21dca_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_972e5a4378c8481ba0572b8b96b21dca_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_972e5a4378c8481ba0572b8b96b21dca_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART C&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_972e5a4378c8481ba0572b8b96b21dca&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_972e5a4378c8481ba0572b8b96b21dca&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;972e5a4378c8481ba0572b8b96b21dca-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;972e5a4378c8481ba0572b8b96b21dca-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;972e5a4378c8481ba0572b8b96b21dca-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_e174ceb337d34715bec9fcdc73042950" class="problems-wrapper" role="group" aria-labelledby="e174ceb337d34715bec9fcdc73042950-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;e174ceb337d34715bec9fcdc73042950-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART D &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@e174ceb337d34715bec9fcdc73042950-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Under the optimal solution, in which of the intersections should a light fixture be placed?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_0-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; Intersection 1 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_1-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; Intersection 2 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_2-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; Intersection 3 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_3-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; Intersection 4 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_4-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; Intersection 5 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1[]&#34; id=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;e174ceb337d34715bec9fcdc73042950_2_1-choice_5-label&#34; for=&#34;input_e174ceb337d34715bec9fcdc73042950_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34;&gt; None &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_e174ceb337d34715bec9fcdc73042950_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_e174ceb337d34715bec9fcdc73042950_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_e174ceb337d34715bec9fcdc73042950_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART D&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_e174ceb337d34715bec9fcdc73042950&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_e174ceb337d34715bec9fcdc73042950&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e174ceb337d34715bec9fcdc73042950-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e174ceb337d34715bec9fcdc73042950-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e174ceb337d34715bec9fcdc73042950-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_264713148c844fe4b4af98e252a0b8d1" class="problems-wrapper" role="group" aria-labelledby="264713148c844fe4b4af98e252a0b8d1-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;264713148c844fe4b4af98e252a0b8d1-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART E &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@264713148c844fe4b4af98e252a0b8d1-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Consider the following new requirements: &lt;/p&gt; &lt;ul&gt; &lt;li&gt;At least one of the corners 1 and 4 must be illuminated with at least 300 units of illumination.&lt;/li&gt; &lt;li&gt;At least three or more of the corners must be illuminated by 150 units of illumination or less.&lt;/li&gt; &lt;li&gt;The luminosity at corner 1 is at most 40% of the luminosity in Corridor B.&lt;/li&gt; &lt;/ul&gt; &lt;ul&gt; &lt;li&gt;\(w\) equals 1 if there is a light bulb at intersection 1 with at least 300 units of luminosity, 0 otherwise.&lt;/li&gt; &lt;li&gt;\(z_i\) equals 1 if the light bulb at intersection i is required to have less at most 150 units of luminosity, 0 otherwise.&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;What are the additional (seven) constraints needed to model these new requirements? &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_0-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_1 \geq 300w\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_1-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_1 \leq 300w\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_2-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_4 \leq 300(1-w)\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_3-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_4 \geq 300(1-w)\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_4-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(w \in \{0,1\}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_5-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_i \leq 150 z_i \forall i \in \{1, \ldots, 5 \}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_6&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_6-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_i \leq 150 (1-z_i) \forall i \in \{1, \ldots, 5 \}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_7&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_7-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(x_i \leq 150 + 150 (1-z_i) \forall i \in \{1, \ldots, 5 \}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_8&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_8&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_8-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_8&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(\sum_{i=1}^5 z_i \geq 3\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_9&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_9&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_9-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_9&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(\sum_{i=1}^5 z_i \leq 3\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_10&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_10&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_10-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_10&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(z_i \in \{0,1\}, \forall i \in \{1, \ldots, 5 \}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_11&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_11&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_11-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_11&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(\frac{x_1}{x_1 + x_3} \leq 0.4\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1[]&#34; id=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_12&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_12&#34;/&gt;&lt;label id=&#34;264713148c844fe4b4af98e252a0b8d1_2_1-choice_12-label&#34; for=&#34;input_264713148c844fe4b4af98e252a0b8d1_2_1_choice_12&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34;&gt; \(0.6 x_1 - 0.4 x_3 \leq 0\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_264713148c844fe4b4af98e252a0b8d1_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_264713148c844fe4b4af98e252a0b8d1_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_264713148c844fe4b4af98e252a0b8d1_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART E&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_264713148c844fe4b4af98e252a0b8d1&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_264713148c844fe4b4af98e252a0b8d1&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;264713148c844fe4b4af98e252a0b8d1-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;264713148c844fe4b4af98e252a0b8d1-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;264713148c844fe4b4af98e252a0b8d1-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-5" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_9a4e29d1054441428c0cd30027b4ae22" class="problems-wrapper" role="group" aria-labelledby="9a4e29d1054441428c0cd30027b4ae22-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;9a4e29d1054441428c0cd30027b4ae22-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART F &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9a4e29d1054441428c0cd30027b4ae22-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Incorporate these new constraints to the original model and solve the problem using Julia and JuMP or Excel. What is the total cost you get under the optimal solution (rounded to the nearest whole number)? Error checking hint. The value is between 4040 and 4065.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; id=&#34;input_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; data-input-id=&#34;9a4e29d1054441428c0cd30027b4ae22_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_9a4e29d1054441428c0cd30027b4ae22_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_9a4e29d1054441428c0cd30027b4ae22_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_9a4e29d1054441428c0cd30027b4ae22_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_9a4e29d1054441428c0cd30027b4ae22_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART F&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_9a4e29d1054441428c0cd30027b4ae22&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_9a4e29d1054441428c0cd30027b4ae22&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9a4e29d1054441428c0cd30027b4ae22-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9a4e29d1054441428c0cd30027b4ae22-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9a4e29d1054441428c0cd30027b4ae22-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-6" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_c7f769dcc63947c2b5e369bf176a346d" class="problems-wrapper" role="group" aria-labelledby="c7f769dcc63947c2b5e369bf176a346d-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;c7f769dcc63947c2b5e369bf176a346d-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART G &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@c7f769dcc63947c2b5e369bf176a346d-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Under the optimal solution, in which of the intersections should a light fixture be placed?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_0-label&#34; for=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; Intersection 1 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_1-label&#34; for=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; Intersection 2 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_2-label&#34; for=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; Intersection 3 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_3-label&#34; for=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; Intersection 4 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_4-label&#34; for=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c7f769dcc63947c2b5e369bf176a346d_2_1&#34;&gt; Intersection 5 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1[]&#34; id=&#34;input_c7f769dcc63947c2b5e369bf176a346d_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;c7f769dcc63947c2b5e369bf176a346d_2_1-choice_5-label&#34; 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@8455ec32319c4b64b5a9dd7006970755" data-block-type="vertical" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="False" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Problem 2</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_1f2e6f2e91f04136804fff0fd0e9ea48" class="problems-wrapper" role="group" aria-labelledby="1f2e6f2e91f04136804fff0fd0e9ea48-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;1f2e6f2e91f04136804fff0fd0e9ea48-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART A &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@1f2e6f2e91f04136804fff0fd0e9ea48-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Factory F produces three different products \( P = \{1, 2, 3\} \) with a single machine. The factory starts operations at 9 AM every morning and ends operations at 5 PM. (Each day has 480 minutes of work.) The machine is configured differently for the three products. To configure the machine to start producing product \( i \in \{1, 2, 3\} \) requires a set-up time (see Table 1). If, for example, the machine were producing product 2, and we would like to switch production to product 1, we would require 45 minutes of set-up time. At the beginning of each day, the machine has to be configured (requires set-up time) regardless of what the last item produced was on the previous day. &lt;/p&gt; &lt;p&gt;The time horizon for this problem is four days. At the end of each day, the factory must meet the demand for each product given in Table 1. If there are items remaining after meeting demand, these items are stored in inventory at a cost of \( h_i \) per unit for product \( i \) (see Table 1). &lt;/p&gt; &lt;p&gt;In the following parts, let \( x_{it} \) denote the time the machine spends on day \( t \) producing item \( i \) for \( i \in P \), and for \( t \in \{1, 2, 3, 4\} \). Let \( y_{it} \) be the number of units of item \( i \) produced on day \( t \), and 0 otherwise. Fractional production units are allowed. Also, the time spent on a day producing an item can be fractional. Let \( z_{it} \) be the variable that tells us if we set up the machine to produce item \( i \) in day \( t \). Let \( s_{it} \) be the amount of product \( i \) that is stored in inventory from the end of day \( t \) to the start of day \( t+1 \) . We require that \( s_{i4} = 0 \) for each \( i \in P \), which means there is no inventory left at the end of day 4. There is no inventory at the beginning of the first day \( (s_{i0} = 0 \) for each \( i \in P \)). &lt;/p&gt; &lt;div id=&#34;tb:1&#34; class=&#34;table&#34;&gt; &lt;center&gt; &lt;table cellspacing=&#34;0&#34; class=&#34;tabular&#34;&gt; &lt;tr&gt; &lt;td style=&#34;text-align:right; border-right:1px solid black&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Set-up Time [min] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Price [$] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Production Rate [units/min] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Inventory Cost [$] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Demand Day 1 [units] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Demand Day 2 [units] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Demand Day 3 [units] &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Demand Day 4 [units] &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; Product 1 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 45 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 50 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 5 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 18 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 400 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 600 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 200 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 800 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; Product 2 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 60 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 70 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 4 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 15 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 240 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 440 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 100 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 660 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; Product 3 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 100 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 120 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 2 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 25 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 80 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 120 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 40 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 100 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;div class=&#34;caption&#34;&gt;&lt;b&gt;Table 1&lt;/b&gt;: &lt;span/&gt;&lt;/div&gt; &lt;label/&gt; &lt;/center&gt; &lt;/div&gt; &lt;p&gt;Formulate a mixed integer program that maximizes the total profits. We let \( d_{it} \) refer to the demand of item \(i \) in day \(t \), and we let \(r_i \) refer to the production rate of product \(i \). These are parameters, not decision variables). &lt;/p&gt; &lt;p&gt;The objective function corresponds to maximizing the total revenue minus the inventory costs. It takes the following form: \( \sum_{i=1}^3 \sum_{t=1}^4 a_i d_{it} - \sum_{i=1}^3 \sum_{t=1}^4 b_i s_{it} \). One can determine \( a_i \) and \( b_i \) for \( i = 1 \text{ to } 3\) from the data. &lt;/p&gt; &lt;p&gt; What is \( a_1 + a_2 + a_3 + b_1 + b_2 + b_3 \)? Error checking hint: the answer is between 290 and 309. &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; id=&#34;input_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; data-input-id=&#34;1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_1f2e6f2e91f04136804fff0fd0e9ea48_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_1f2e6f2e91f04136804fff0fd0e9ea48_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_1f2e6f2e91f04136804fff0fd0e9ea48_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART A&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_1f2e6f2e91f04136804fff0fd0e9ea48&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_1f2e6f2e91f04136804fff0fd0e9ea48&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;1f2e6f2e91f04136804fff0fd0e9ea48-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;1f2e6f2e91f04136804fff0fd0e9ea48-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;1f2e6f2e91f04136804fff0fd0e9ea48-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_b49465f876e649c8a93adcb941d42863" class="problems-wrapper" role="group" aria-labelledby="b49465f876e649c8a93adcb941d42863-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="2.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;b49465f876e649c8a93adcb941d42863-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART B &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@b49465f876e649c8a93adcb941d42863-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; The constraint for machine usage time limit for day t in minutes is \( az_{1t} + bz_{2t} + cz_{3t} + d \sum_{i=1}^3 x_{it} \leq e. \) You can obtain the coefficients by looking at the data. What is \( a + b + c + d + e? \) Error checking hint. The value is between 680 and 699. &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_b49465f876e649c8a93adcb941d42863_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_b49465f876e649c8a93adcb941d42863_2_1&#34; id=&#34;input_b49465f876e649c8a93adcb941d42863_2_1&#34; data-input-id=&#34;b49465f876e649c8a93adcb941d42863_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_b49465f876e649c8a93adcb941d42863_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_b49465f876e649c8a93adcb941d42863_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_b49465f876e649c8a93adcb941d42863_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_b49465f876e649c8a93adcb941d42863_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_b49465f876e649c8a93adcb941d42863_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_b49465f876e649c8a93adcb941d42863_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART B&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_b49465f876e649c8a93adcb941d42863&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_b49465f876e649c8a93adcb941d42863&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;b49465f876e649c8a93adcb941d42863-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;b49465f876e649c8a93adcb941d42863-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;b49465f876e649c8a93adcb941d42863-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_c9fdce093ae54d0bbc526a3953b16051" class="problems-wrapper" role="group" aria-labelledby="c9fdce093ae54d0bbc526a3953b16051-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;c9fdce093ae54d0bbc526a3953b16051-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART C &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@c9fdce093ae54d0bbc526a3953b16051-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;The inventory of item i from at the end of day t is equal to the initial stock of day t - 1 plus the production in day t minus the demand in day t.&lt;/p&gt; &lt;p&gt;Choose all necessary constraint(s) to model inventory balance below. Your answer should include four sets of constraints. &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_0-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{it-1} + y_{it} = s_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_1-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{it-1} + y_{it} -d_{it} = s_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_2-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{it-1} + y_{it} +d_{it} = s_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_3-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( d_{it} = 0, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_4-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{i0} = 0, \forall i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_5-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{i1} \le 0, \forall i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_6&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_6-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{i4} \le 0, \forall i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_7&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_7-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{i4} = 0, \forall i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1[]&#34; id=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_8&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_8&#34;/&gt;&lt;label id=&#34;c9fdce093ae54d0bbc526a3953b16051_2_1-choice_8-label&#34; for=&#34;input_c9fdce093ae54d0bbc526a3953b16051_2_1_choice_8&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;&gt; \( s_{it} \ge 0, \forall t=1,\ldots,4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_c9fdce093ae54d0bbc526a3953b16051_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_c9fdce093ae54d0bbc526a3953b16051_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_c9fdce093ae54d0bbc526a3953b16051_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART C&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_c9fdce093ae54d0bbc526a3953b16051&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_c9fdce093ae54d0bbc526a3953b16051&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;c9fdce093ae54d0bbc526a3953b16051-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;c9fdce093ae54d0bbc526a3953b16051-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;c9fdce093ae54d0bbc526a3953b16051-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_221601c37b544b1081d1916b618c33b8" class="problems-wrapper" role="group" aria-labelledby="221601c37b544b1081d1916b618c33b8-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;221601c37b544b1081d1916b618c33b8-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART D &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@221601c37b544b1081d1916b618c33b8-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Please select the remaining constraint(s) that are needed for the formulation to be correct. Select 4 sets of constraints.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_0-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it} \ge Mz_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_1-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it} \le Mz_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_2-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it} = Mz_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_3-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( y_{it} = r_i x_{it}, \forall t = 1, \dots, 4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_4-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( y_{it} \ge r_i x_{it}, \forall t=1,\ldots,4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_5-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it} = r_i y_{it}, \forall t=1,\ldots,4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_6&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_6-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it} \ge r_i y_{it}, \forall t=1,\ldots,4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_7&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_7-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( z_{it} \in \{0,1\} \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_221601c37b544b1081d1916b618c33b8_2_1[]&#34; id=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_8&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_8&#34;/&gt;&lt;label id=&#34;221601c37b544b1081d1916b618c33b8_2_1-choice_8-label&#34; for=&#34;input_221601c37b544b1081d1916b618c33b8_2_1_choice_8&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34;&gt; \( x_{it}, y_{it} \ge 0, \forall t=1,\ldots,4, i=1, \ldots, 3 \) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_221601c37b544b1081d1916b618c33b8_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_221601c37b544b1081d1916b618c33b8_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_221601c37b544b1081d1916b618c33b8_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART D&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_221601c37b544b1081d1916b618c33b8&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_221601c37b544b1081d1916b618c33b8&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;221601c37b544b1081d1916b618c33b8-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;221601c37b544b1081d1916b618c33b8-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;221601c37b544b1081d1916b618c33b8-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_dd66fd4e0a7d46fe9d5c156b056b6eb8" class="problems-wrapper" role="group" aria-labelledby="dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART E &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Solve the production problem you formulated from parts (a) to (d) using Julia and JuMP. What&amp;#8217;s the optimal objective value (net revenue minus inventory costs)? Error checking hint. The value is between 238000 amd 239000.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; id=&#34;input_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; data-input-id=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_dd66fd4e0a7d46fe9d5c156b056b6eb8_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_dd66fd4e0a7d46fe9d5c156b056b6eb8_solution_1&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART E&#34; /&gt; &lt;div class=&#34;problem-hint&#34;&gt; &lt;div class=&#34;notification problem-hint notification-hint is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn hint-button&#34;&gt; Next Hint &lt;/button&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_dd66fd4e0a7d46fe9d5c156b056b6eb8&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_dd66fd4e0a7d46fe9d5c156b056b6eb8&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;hint-button problem-action-btn btn-default btn-small&#34; data-value=&#34;Hint&#34; &gt;&lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt;Hint&lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd66fd4e0a7d46fe9d5c156b056b6eb8-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-5" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_2340a7308e0c4e919fc7e2be80c74651" class="problems-wrapper" role="group" aria-labelledby="2340a7308e0c4e919fc7e2be80c74651-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;2340a7308e0c4e919fc7e2be80c74651-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART F &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@2340a7308e0c4e919fc7e2be80c74651-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Using the original given values, consider that it is possible to have a Super Production (SP) day in which there are an extra 2 hours in the day. The extra two hours costs $50 because of increased labor costs. The factory can have up to two SP days out of four, but the two days cannot be consecutive. Formulate the modified machine scheduling problems as a mixed integer linear program. Let \(u_t\) for t = 1, 2, 3, 4 be the extra decision variables. \(u_t = 1\) means that day \(t\) is a super production day; \(u_t = 0\), otherwise.&lt;/p&gt; &lt;p&gt;The new objective function we want to maximize for total profit is: \( \sum_{i=1}^3 \sum_{t=1}^4 a_i d_{it} - \sum_{i=1}^3 \sum_{t=1}^4 b_i s_{it} - c \sum_{t=1}^4 u_t \).&lt;/p&gt; &lt;p&gt; What is \(c?\) There is no error checking hint for this problem. &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; id=&#34;input_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; data-input-id=&#34;2340a7308e0c4e919fc7e2be80c74651_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_2340a7308e0c4e919fc7e2be80c74651_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_2340a7308e0c4e919fc7e2be80c74651_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_2340a7308e0c4e919fc7e2be80c74651_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_2340a7308e0c4e919fc7e2be80c74651_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART F&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_2340a7308e0c4e919fc7e2be80c74651&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_2340a7308e0c4e919fc7e2be80c74651&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2340a7308e0c4e919fc7e2be80c74651-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2340a7308e0c4e919fc7e2be80c74651-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2340a7308e0c4e919fc7e2be80c74651-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-6" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_cdf85475b32a4cbe92c071f28b347d5a" class="problems-wrapper" role="group" aria-labelledby="cdf85475b32a4cbe92c071f28b347d5a-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;cdf85475b32a4cbe92c071f28b347d5a-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART G &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@cdf85475b32a4cbe92c071f28b347d5a-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Choose the correct 4 sets of constraints that should be added (replaced):&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_0-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( 45z_{1t} + 60z_{2t} + 100z_{3t} + \sum_{i=1}^3 x_{it} \leq 480 + u_t, \forall t = 1, \dots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_1-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( 45z_{1t} + 60z_{2t} + 100z_{3t} + \sum_{i=1}^3 x_{it} \leq 480 + 120u_t, \forall t = 1, \dots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_2-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( \sum_{t=1}^4 u_t \geq 2 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_3-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( \sum_{t=1}^4 u_t \leq 2 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_4-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( u_t \leq 1, \forall t=1, \ldots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_5-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( u_t = 0, \forall t=1, \ldots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_6&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_6-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( u_{t-1} + u_t \leq 1, \forall t=2, \ldots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1[]&#34; id=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_7&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;cdf85475b32a4cbe92c071f28b347d5a_2_1-choice_7-label&#34; for=&#34;input_cdf85475b32a4cbe92c071f28b347d5a_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;&gt; \( u_{t} \in \{0,1\}, \forall t=1, \ldots, 4 \) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_cdf85475b32a4cbe92c071f28b347d5a_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_cdf85475b32a4cbe92c071f28b347d5a_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART G&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_cdf85475b32a4cbe92c071f28b347d5a&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_cdf85475b32a4cbe92c071f28b347d5a&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;cdf85475b32a4cbe92c071f28b347d5a-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;cdf85475b32a4cbe92c071f28b347d5a-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;cdf85475b32a4cbe92c071f28b347d5a-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-7" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_6e936a1540e4433182a1a6a6d12581d4" class="problems-wrapper" role="group" aria-labelledby="6e936a1540e4433182a1a6a6d12581d4-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;6e936a1540e4433182a1a6a6d12581d4-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART H &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@6e936a1540e4433182a1a6a6d12581d4-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Solve the production problem under Super Production Days you formulated above in PARTS A to G using Julia and JuMP. What&amp;#8217;s the optimal objective value? Error checking hint: it is between 240000 and 241900.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; id=&#34;input_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; data-input-id=&#34;6e936a1540e4433182a1a6a6d12581d4_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_6e936a1540e4433182a1a6a6d12581d4_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_6e936a1540e4433182a1a6a6d12581d4_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_6e936a1540e4433182a1a6a6d12581d4_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_6e936a1540e4433182a1a6a6d12581d4_solution_1&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART H&#34; /&gt; &lt;div class=&#34;problem-hint&#34;&gt; &lt;div class=&#34;notification problem-hint notification-hint is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;6e936a1540e4433182a1a6a6d12581d4-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn hint-button&#34;&gt; Next Hint &lt;/button&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_6e936a1540e4433182a1a6a6d12581d4&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_6e936a1540e4433182a1a6a6d12581d4&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;hint-button problem-action-btn btn-default btn-small&#34; data-value=&#34;Hint&#34; &gt;&lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt;Hint&lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;6e936a1540e4433182a1a6a6d12581d4-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;6e936a1540e4433182a1a6a6d12581d4-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;6e936a1540e4433182a1a6a6d12581d4-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-8" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_12d1534152b54bf780957941d24814c9" class="problems-wrapper" role="group" aria-labelledby="12d1534152b54bf780957941d24814c9-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;12d1534152b54bf780957941d24814c9-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART I &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@12d1534152b54bf780957941d24814c9-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;What days are SP days under the optimal solution? Check all that apply &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_12d1534152b54bf780957941d24814c9_2_1[]&#34; id=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;12d1534152b54bf780957941d24814c9_2_1-choice_0-label&#34; for=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; Day 1 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_12d1534152b54bf780957941d24814c9_2_1[]&#34; id=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;12d1534152b54bf780957941d24814c9_2_1-choice_1-label&#34; for=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; Day 2 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_12d1534152b54bf780957941d24814c9_2_1[]&#34; id=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;12d1534152b54bf780957941d24814c9_2_1-choice_2-label&#34; for=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; Day 3 &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_12d1534152b54bf780957941d24814c9_2_1[]&#34; id=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;12d1534152b54bf780957941d24814c9_2_1-choice_3-label&#34; for=&#34;input_12d1534152b54bf780957941d24814c9_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34;&gt; Day 4 &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_12d1534152b54bf780957941d24814c9_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_12d1534152b54bf780957941d24814c9_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_12d1534152b54bf780957941d24814c9_solution_1&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART I&#34; /&gt; &lt;div class=&#34;problem-hint&#34;&gt; &lt;div class=&#34;notification problem-hint notification-hint is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;12d1534152b54bf780957941d24814c9-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn hint-button&#34;&gt; Next Hint &lt;/button&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_12d1534152b54bf780957941d24814c9&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_12d1534152b54bf780957941d24814c9&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;span class=&#34;problem-action-button-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;hint-button problem-action-btn btn-default btn-small&#34; data-value=&#34;Hint&#34; &gt;&lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt;Hint&lt;/button&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;12d1534152b54bf780957941d24814c9-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;12d1534152b54bf780957941d24814c9-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;12d1534152b54bf780957941d24814c9-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@68cbc62eee214f49b532ad5be67e1444" data-block-type="vertical" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="False" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Problem 3</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_565b0a15516444099c46e2168e480b4b" class="problems-wrapper" role="group" aria-labelledby="565b0a15516444099c46e2168e480b4b-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;565b0a15516444099c46e2168e480b4b-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART A &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@565b0a15516444099c46e2168e480b4b-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Sudoku is a popular number puzzle. The goal is to place the digits in [1,9] on a nine-by-nine grid, with some of the digits already filled in, where [1,9] denotes the set of integers from 1 to 9. Your solution must satisfy the following four rules:&lt;/p&gt; &lt;ul&gt; &lt;li&gt;Rule 1. Each cell contains an integer in [1,9]. &lt;/li&gt; &lt;li&gt;Rule 2. Each row must contain each of the integers in [1,9]. &lt;/li&gt; &lt;li&gt;Rule 3. Each column must contain each of the integers in [1,9].&lt;/li&gt; &lt;li&gt;Rule 4. Each of the nine 3x3 squares with bold outlines must contain each of the integers in [1,9].&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;Figure 1 below presents a Sudoku puzzle. Figure 2 presents the solved Sudoku puzzle in which all four of the rules are satisfied.&lt;/p&gt; &lt;p&gt; &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/cad860c72b18df7baa8139563b53237b/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudoku1.png&#34;&gt; &lt;img width=&#34;390&#34; height=&#34;392&#34; alt=&#34;SudokuEmpty&#34; src=&#34;/assets/courseware/v1/cad860c72b18df7baa8139563b53237b/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudoku1.png&#34;/&gt; &lt;/a&gt; &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/eae86c4e58eb68237d07ecae971472ee/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudoku2.png&#34;&gt; &lt;img width=&#34;390&#34; height=&#34;392&#34; alt=&#34;Sudoku&#34; src=&#34;/assets/courseware/v1/eae86c4e58eb68237d07ecae971472ee/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudoku2.png&#34;/&gt; &lt;/a&gt; &lt;/p&gt; &lt;p&gt;Sudoku isn&amp;#8217;t an optimization problem, it&amp;#8217;s actually a feasibility problem: we wish to find a feasible solution that satisfies these rules. You can think of it as an optimization problem in which the objective is always equal to 0. This problem firsts asks you to use integer programming formulation techniques to model the rules of Sudoku. It then asks you to solve it using Julia and JuMP.&lt;/p&gt; &lt;p&gt;Model this problem using integer programming. Define binary variable \(x_{ijk} \in \{0,1\} , \forall i=1,\ldots,9, j=1,\ldots,9, k = 1,\ldots, 9 \), which equals to 1 if we put number \( k \) in the \(i^{th}\) row and \(j^{th}\) column and 0 otherwise. &lt;/p&gt; &lt;p&gt; Let \( a_{ijk} = 1 \) if the initial puzzle has a \( k \) in row \( i \) and column \( j \). Otherwise, \( a_{ijk} = 0 \). &lt;/p&gt; &lt;p&gt; The following constraints model the Sudoku problem.&lt;/p&gt; &lt;p&gt; C1. \( x_{ijk} \ge a_{ijk}, \\ \forall i=1,\ldots, 9, j=1,\ldots, 9, k= 1, \ldots, 9 \) &lt;/p&gt; &lt;p&gt; C2. \( \sum_{i=1}^9 x_{ijk}=1, \\ \forall j=1,\ldots, 9, k= 1, \ldots, 9 \) &lt;/p&gt; &lt;p&gt; C3. \( \sum_{j=1}^9 x_{ijk}=1, \\ \forall i=1,\ldots, 9, k= 1, \ldots, 9 \) &lt;/p&gt; &lt;p&gt; C4. \( \sum_{k=1}^9 x_{ijk}=1, \\ \forall i=1,\ldots, 9, j= 1, \ldots, 9 \) &lt;/p&gt; &lt;p&gt; C5. \( \sum_{a \in \{1,2,3\}, b \in \{1,2,3\}} X_{(3i+a),(3j+b),k} =1, \\ \forall i \in \{0, 1, 2\}, j \in \{0, 1, 2\}, k = 1, \ldots, 9 \) &lt;/p&gt; &lt;p&gt;C2 models which rule?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_565b0a15516444099c46e2168e480b4b_2_1&#34; id=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;565b0a15516444099c46e2168e480b4b_2_1-choice_0-label&#34; for=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; Rule 1&amp;#160; &amp;#160;(rule for cells) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_565b0a15516444099c46e2168e480b4b_2_1&#34; id=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;565b0a15516444099c46e2168e480b4b_2_1-choice_1-label&#34; for=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; Rule 2&amp;#160; &amp;#160;(rule for rows) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_565b0a15516444099c46e2168e480b4b_2_1&#34; id=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;565b0a15516444099c46e2168e480b4b_2_1-choice_2-label&#34; for=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; Rule 3&amp;#160; (rule for columns) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_565b0a15516444099c46e2168e480b4b_2_1&#34; id=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;565b0a15516444099c46e2168e480b4b_2_1-choice_3-label&#34; for=&#34;input_565b0a15516444099c46e2168e480b4b_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34;&gt; Rule 4.&amp;#160; (rule for 3 x 3 squares) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_565b0a15516444099c46e2168e480b4b_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_565b0a15516444099c46e2168e480b4b_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_565b0a15516444099c46e2168e480b4b_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART A&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_565b0a15516444099c46e2168e480b4b&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_565b0a15516444099c46e2168e480b4b&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;565b0a15516444099c46e2168e480b4b-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;565b0a15516444099c46e2168e480b4b-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;565b0a15516444099c46e2168e480b4b-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_4f80d62055fd45be9915d9295a483961" class="problems-wrapper" role="group" aria-labelledby="4f80d62055fd45be9915d9295a483961-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;4f80d62055fd45be9915d9295a483961-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART B &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@4f80d62055fd45be9915d9295a483961-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;C3 models which rule?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4f80d62055fd45be9915d9295a483961_2_1&#34; id=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;4f80d62055fd45be9915d9295a483961_2_1-choice_0-label&#34; for=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; Rule 1&amp;#160; &amp;#160;(rule for cells) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4f80d62055fd45be9915d9295a483961_2_1&#34; id=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;4f80d62055fd45be9915d9295a483961_2_1-choice_1-label&#34; for=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; Rule 2&amp;#160; &amp;#160;(rule for rows) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4f80d62055fd45be9915d9295a483961_2_1&#34; id=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;4f80d62055fd45be9915d9295a483961_2_1-choice_2-label&#34; for=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; Rule 3&amp;#160; (rule for columns) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4f80d62055fd45be9915d9295a483961_2_1&#34; id=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;4f80d62055fd45be9915d9295a483961_2_1-choice_3-label&#34; for=&#34;input_4f80d62055fd45be9915d9295a483961_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34;&gt; Rule 4.&amp;#160; (rule for 3 x 3 squares) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_4f80d62055fd45be9915d9295a483961_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_4f80d62055fd45be9915d9295a483961_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_4f80d62055fd45be9915d9295a483961_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART B&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_4f80d62055fd45be9915d9295a483961&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_4f80d62055fd45be9915d9295a483961&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4f80d62055fd45be9915d9295a483961-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4f80d62055fd45be9915d9295a483961-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4f80d62055fd45be9915d9295a483961-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_261073458036442d8e57fb06a58565ed" class="problems-wrapper" role="group" aria-labelledby="261073458036442d8e57fb06a58565ed-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;261073458036442d8e57fb06a58565ed-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART C &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@261073458036442d8e57fb06a58565ed-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;C4 models which rule?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_261073458036442d8e57fb06a58565ed_2_1&#34; id=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;261073458036442d8e57fb06a58565ed_2_1-choice_0-label&#34; for=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; Rule 1&amp;#160; &amp;#160;(rule for cells) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_261073458036442d8e57fb06a58565ed_2_1&#34; id=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;261073458036442d8e57fb06a58565ed_2_1-choice_1-label&#34; for=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; Rule 2&amp;#160; &amp;#160;(rule for rows) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_261073458036442d8e57fb06a58565ed_2_1&#34; id=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;261073458036442d8e57fb06a58565ed_2_1-choice_2-label&#34; for=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; Rule 3&amp;#160; (rule for columns) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_261073458036442d8e57fb06a58565ed_2_1&#34; id=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;261073458036442d8e57fb06a58565ed_2_1-choice_3-label&#34; for=&#34;input_261073458036442d8e57fb06a58565ed_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34;&gt; Rule 4.&amp;#160; (rule for 3 x 3 squares) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_261073458036442d8e57fb06a58565ed_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_261073458036442d8e57fb06a58565ed_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_261073458036442d8e57fb06a58565ed_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART C&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_261073458036442d8e57fb06a58565ed&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_261073458036442d8e57fb06a58565ed&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;261073458036442d8e57fb06a58565ed-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;261073458036442d8e57fb06a58565ed-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;261073458036442d8e57fb06a58565ed-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_dbc9bdc6b8ff4094bf5e8c5829358a1a" class="problems-wrapper" role="group" aria-labelledby="dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART D &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;C5 models which rule?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34; id=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1-choice_0-label&#34; for=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; Rule 1&amp;#160; &amp;#160;(rule for cells) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34; id=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1-choice_1-label&#34; for=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; Rule 2&amp;#160; &amp;#160;(rule for rows) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34; id=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1-choice_2-label&#34; for=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; Rule 3&amp;#160; (rule for columns) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34; id=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1-choice_3-label&#34; for=&#34;input_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;&gt; Rule 4.&amp;#160; (rule for 3 x 3 squares) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_dbc9bdc6b8ff4094bf5e8c5829358a1a_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_dbc9bdc6b8ff4094bf5e8c5829358a1a_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART D&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_dbc9bdc6b8ff4094bf5e8c5829358a1a&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_dbc9bdc6b8ff4094bf5e8c5829358a1a&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dbc9bdc6b8ff4094bf5e8c5829358a1a-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_beb0b5ab62d2401994bf7ed256500ada" class="problems-wrapper" role="group" aria-labelledby="beb0b5ab62d2401994bf7ed256500ada-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="2.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;beb0b5ab62d2401994bf7ed256500ada-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART E &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@beb0b5ab62d2401994bf7ed256500ada-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Solve the feasibility problem you formulated using Julia and JuMP and what is the value of \( A + B + C \) in your solution?&lt;/p&gt; &lt;p&gt; &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/98426e72aaf4c8be1e9444a0b0bd3d44/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudokuabc.png&#34;&gt; &lt;img width=&#34;544&#34; height=&#34;544&#34; alt=&#34;Sudoku&#34; src=&#34;/assets/courseware/v1/98426e72aaf4c8be1e9444a0b0bd3d44/asset-v1:MITx+15.053x+3T2016+type@asset+block/sudokuabc.png&#34;/&gt; &lt;/a&gt; &lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; id=&#34;input_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; data-input-id=&#34;beb0b5ab62d2401994bf7ed256500ada_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_beb0b5ab62d2401994bf7ed256500ada_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_beb0b5ab62d2401994bf7ed256500ada_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_beb0b5ab62d2401994bf7ed256500ada_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_beb0b5ab62d2401994bf7ed256500ada_solution_1&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART E&#34; /&gt; &lt;div class=&#34;problem-hint&#34;&gt; &lt;div class=&#34;notification problem-hint notification-hint is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-question&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;beb0b5ab62d2401994bf7ed256500ada-problem-title&#34;&gt; 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<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@0a04ca54e6dc4d2db59c82c1a6deb575" data-block-type="vertical" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="False" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Problem 4</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_4d9dbd0a246a42a98b6e9c9942f9b908" class="problems-wrapper" role="group" aria-labelledby="4d9dbd0a246a42a98b6e9c9942f9b908-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;4d9dbd0a246a42a98b6e9c9942f9b908-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART A &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@4d9dbd0a246a42a98b6e9c9942f9b908-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;We now analyze the problem of a firm trying to decide on the opening of several lockboxes. In this problem we have to take into account the binary decisions of opening/not opening each potential lockbox, as well as an assignment problem to decide which regions should send their money to each lockbox. There are fixed costs for opening a lockbox, and there are opportunity costs for not opening a lockbox. This problem is based on an example from: G. Cornu&amp;#233;jols and R. T&amp;#252;t&amp;#252;nc&amp;#252;, &lt;i&gt;Optimization Methods in Finance.&lt;/i&gt;&lt;/p&gt; &lt;p&gt;Consider a national firm that receives checks from all over the United States. Due to the vagaries of the U.S. Postal Service, as well as the banking system, there is a variable delay from when the check is postmarked (and hence the customer has met her obligation) and when the check clears (and when the firm can use the money). For instance, a check mailed in Boston sent to a Boston address might clear in just 3 days. A similar check sent to Los Angeles might take 7 days to clear. It is in the firm&amp;#8217;s interest to have the check clear as quickly as possible since then the firm can use the money. In order to speed up this clearing process, firms open offices (called lockboxes) in different cities to handle the checks.&lt;/p&gt; &lt;p&gt;For example, suppose we receive payments from 3 regions (West, East, and South). The average daily value from each region is as follows: $625,000 from the West, $850,000 from the East, and $350,000 from the South. We are considering opening lockboxes in Los Angeles, Chicago, and/or Boston. Operating a lockbox costs $150,000 per year. Currently, all checks are mailed to Seattle, where the firm is based. We can assume that handling checks in Seattle does not cost extra money. The average days from mailing to clearing is given in Table 1. Which lockboxes should we open?&lt;/p&gt; &lt;center&gt; &lt;table&gt; &lt;tbody&gt; &lt;tr&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;/&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;L.A.&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Chicago&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Boston&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Seattle&lt;/th&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;West&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;2&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;4&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;6&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;2&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;East&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;7&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;5&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;3&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;6&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;South&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;4&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;5&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;6&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;5&lt;/td&gt; &lt;/tr&gt; &lt;/tbody&gt; &lt;caption&gt;Table 1: Average clearing times for checks mailed from one region to L.A., Chicago, Boston, and Seattle.&lt;/caption&gt; &lt;/table&gt; &lt;/center&gt; &lt;p/&gt; &lt;p&gt;First we must calculate the lost interest for each possible assignment. For example, if the West sends its checks to a lockbox in Boston, then on average there will be $3,750,000 (= 6 x $625,000) in process on any given day. Assuming a fixed investment rate of 6%, this corresponds to a yearly loss of $225,000. We can calculate the losses for the other combinations in a similar fashion; we obtain Table 2. &lt;/p&gt; &lt;center&gt; &lt;table&gt; &lt;tbody&gt; &lt;tr&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;/&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;L.A.&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Chicago&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Boston&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Seattle&lt;/th&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;West&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;75&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;150&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;225&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;75&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;East&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;357&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;255&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;153&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;306&lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;th scope=&#34;row&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;South&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;84&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;105&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;126&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;105&lt;/td&gt; &lt;/tr&gt; &lt;/tbody&gt; &lt;caption&gt;Table 2: Yearly opportunity cost in thousands of US dollars for checks sent from West, East, South to L.A., Chicago, Boston, and Seattle.&lt;/caption&gt; &lt;/table&gt; &lt;/center&gt; &lt;p/&gt; &lt;p&gt;We can open as many lockboxes as we need. Our goal is to determine the decision that minimizes total costs for the firm: how many lockboxes should be opened, and where. Note that this problem is an integer linear program. We will use the following variables. Let \(y_j\) be a binary variable that is 1 if lockbox \(j\) is opened and 0 if it is not, \(j = 1,\ldots,3\) (L.A., Chicago, Boston). Note that checks can always be handled in Seattle: there is no cost associated to opening a lockbox in Seattle. Let \(x_{ij}\) be 1 if region \(i\) sends its checks to lockbox \(j, i = 1, \ldots, 3 \) (West, East, South) and \(j = 1,\ldots, 4 \) (\(j = 4\) corresponding to Seattle). &lt;/p&gt; &lt;p&gt;Formulate the objective function of the problem, taking into account the cost of opening lockboxes and opportunity costs due to lost interest. As mentioned in the problem&amp;#8217;s description, we can assume that checks can be handed in Seattle without having to pay extra for opening a lockbox there.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34; id=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;4d9dbd0a246a42a98b6e9c9942f9b908_2_1-choice_3-label&#34; for=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; MIN \( 150 (y_{1} + y_{2} + y_{3}) + 75x_{11} + 150x_{12} + 225x_{13} + 75x_{14} + 357x_{21}\\ + 255x_{22} + 153x_{23} + 306x_{24} + 84x_{31} + 105x_{32} + 126x_{33} + 105x_{34}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34; id=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;4d9dbd0a246a42a98b6e9c9942f9b908_2_1-choice_1-label&#34; for=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; MAX \( 150 (y_{1} + y_{2} + y_{3}) + 75x_{11} + 150x_{21} + 225x_{31} + 75x_{41}\\ + 357x_{12} + 255x_{22} + 153x_{32} + 306x_{42} + 84x_{13} + 105x_{23} + 126x_{33} + 105x_{43}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34; id=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;4d9dbd0a246a42a98b6e9c9942f9b908_2_1-choice_2-label&#34; for=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; MAX \( 150 (y_{1} + y_{2} + y_{3}) \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34; id=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;4d9dbd0a246a42a98b6e9c9942f9b908_2_1-choice_0-label&#34; for=&#34;input_4d9dbd0a246a42a98b6e9c9942f9b908_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;&gt; MIN \( 75x_{{11}} + 150x_{{12}} + 225x_{{13}} + 75x_{{14}} + 357x_{{21}} + 255x_{22} + 153x_{23} + 306x_{24} \\ + 84x_{31} + 105x_{32} + 126x_{33} + 105x_{34}\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_4d9dbd0a246a42a98b6e9c9942f9b908_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_4d9dbd0a246a42a98b6e9c9942f9b908_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART A&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_4d9dbd0a246a42a98b6e9c9942f9b908&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_4d9dbd0a246a42a98b6e9c9942f9b908&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4d9dbd0a246a42a98b6e9c9942f9b908-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4d9dbd0a246a42a98b6e9c9942f9b908-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;4d9dbd0a246a42a98b6e9c9942f9b908-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_9e4a7f6dbb444d5db3385ddcd6d4525b" class="problems-wrapper" role="group" aria-labelledby="9e4a7f6dbb444d5db3385ddcd6d4525b-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART B &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9e4a7f6dbb444d5db3385ddcd6d4525b-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Formulate the constraints that a region cannot send checks to a closed lockbox. &lt;i&gt;Hint: For each region \(i\) and for each lockbox \(j\), add a constraint that is equivalent to &amp;#8220;if \(x_{ij} = 1\), then \(y_j = 1\)&amp;#8221;&lt;/i&gt;. There are two correct ways of formulating these constraints. Select both of them below.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1[]&#34; id=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b_2_1-choice_0-label&#34; for=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;text&gt; &lt;p class=&#34;equation&#34;&gt;\[\left.\begin{array}{rrcl} &amp;amp; x_{11} + x_{21} + x_{31} \leq 3y_1 \\ &amp;amp; x_{12} + x_{22} + x_{32} \leq 3y_2 \\ &amp;amp; x_{13} + x_{23} + x_{33} \leq 3y_3 \end{array}\right\}\]&lt;/p&gt; &lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1[]&#34; id=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b_2_1-choice_1-label&#34; for=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;text&gt; &lt;p class=&#34;equation&#34;&gt;\[\left.\begin{array}{rrcl} &amp;amp; x_{11} + x_{21} + x_{31} \geq 3y_1 \\ &amp;amp; x_{12} + x_{22} + x_{32} \geq 3y_2 \\ &amp;amp; x_{13} + x_{23} + x_{33} \geq 3y_3 \end{array}\right\}\]&lt;/p&gt; &lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1[]&#34; id=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b_2_1-choice_2-label&#34; for=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;text&gt; &lt;p class=&#34;equation&#34;&gt;\[\left.\begin{array}{rrcl} &amp;amp; x_{11} \leq y_1 &amp;amp; x_{21} \leq y_1 &amp;amp; x_{31} \leq y_1 \\ &amp;amp; x_{12} \leq y_2 &amp;amp; x_{22} \leq y_2 &amp;amp; x_{32} \leq y_2 \\ &amp;amp; x_{13} \leq y_3 &amp;amp; x_{23} \leq y_3 &amp;amp; x_{33} \leq y_3 \end{array}\right\}\]&lt;/p&gt; &lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1[]&#34; id=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b_2_1-choice_3-label&#34; for=&#34;input_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;&gt; &lt;text&gt; &lt;p class=&#34;equation&#34;&gt;\[\left.\begin{array}{rrcl} &amp;amp; x_{11} \geq y_1 &amp;amp; x_{21} \geq y_1 &amp;amp; x_{31} \geq y_1 \\ &amp;amp; x_{12} \geq y_2 &amp;amp; x_{22} \geq y_2 &amp;amp; x_{32} \geq y_2 \\ &amp;amp; x_{13} \geq y_3 &amp;amp; x_{23} \geq y_3 &amp;amp; x_{33} \geq y_3 \end{array}\right\}\]&lt;/p&gt; &lt;/text&gt; &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_9e4a7f6dbb444d5db3385ddcd6d4525b_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_9e4a7f6dbb444d5db3385ddcd6d4525b_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART B&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_9e4a7f6dbb444d5db3385ddcd6d4525b&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_9e4a7f6dbb444d5db3385ddcd6d4525b&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9e4a7f6dbb444d5db3385ddcd6d4525b-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_f16b79c469554a1d9e7646cfdc798d98" class="problems-wrapper" role="group" aria-labelledby="f16b79c469554a1d9e7646cfdc798d98-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;f16b79c469554a1d9e7646cfdc798d98-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART C &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@f16b79c469554a1d9e7646cfdc798d98-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;There are constraints that ensure that the checks from each region are mailed to a lock box.&lt;/p&gt; &lt;p&gt;Which of the constraints below is the &#34;West-assigned region constraint&#34;?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1&#34; id=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#D&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1a#D&#34;/&gt;&lt;label id=&#34;f16b79c469554a1d9e7646cfdc798d98_2_1-choice_1a#D-label&#34; for=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#D&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; \( x_{11} + x_{21} + x_{31} + x_{41} \leq 1\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1&#34; id=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#B&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1a#B&#34;/&gt;&lt;label id=&#34;f16b79c469554a1d9e7646cfdc798d98_2_1-choice_1a#B-label&#34; for=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#B&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; \( x_{11} + x_{12} + x_{13} + x_{14} \leq 1\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1&#34; id=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#C&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1a#C&#34;/&gt;&lt;label id=&#34;f16b79c469554a1d9e7646cfdc798d98_2_1-choice_1a#C-label&#34; for=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#C&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; \( x_{11} + x_{21} + x_{31} + x_{41} = 1\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1&#34; id=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#A&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1a#A&#34;/&gt;&lt;label id=&#34;f16b79c469554a1d9e7646cfdc798d98_2_1-choice_1a#A-label&#34; for=&#34;input_f16b79c469554a1d9e7646cfdc798d98_2_1_choice_1a#A&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;&gt; \( x_{11} + x_{12} + x_{13} + x_{14} = 1\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_f16b79c469554a1d9e7646cfdc798d98_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_f16b79c469554a1d9e7646cfdc798d98_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_f16b79c469554a1d9e7646cfdc798d98_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART C&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_f16b79c469554a1d9e7646cfdc798d98&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_f16b79c469554a1d9e7646cfdc798d98&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;f16b79c469554a1d9e7646cfdc798d98-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;f16b79c469554a1d9e7646cfdc798d98-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;f16b79c469554a1d9e7646cfdc798d98-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_d8c78cccb0d44600a8a5bdde4184712e" class="problems-wrapper" role="group" aria-labelledby="d8c78cccb0d44600a8a5bdde4184712e-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;d8c78cccb0d44600a8a5bdde4184712e-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART D &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@d8c78cccb0d44600a8a5bdde4184712e-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Formulate this instance of the Lockbox Problem in Excel, and solve it using Solver or OpenSolver. What is the optimal cost? Error checking hint. It is between 480 and 495.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; id=&#34;input_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; data-input-id=&#34;d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_d8c78cccb0d44600a8a5bdde4184712e_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_d8c78cccb0d44600a8a5bdde4184712e_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_d8c78cccb0d44600a8a5bdde4184712e_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART D&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_d8c78cccb0d44600a8a5bdde4184712e&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_d8c78cccb0d44600a8a5bdde4184712e&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;d8c78cccb0d44600a8a5bdde4184712e-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;d8c78cccb0d44600a8a5bdde4184712e-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;d8c78cccb0d44600a8a5bdde4184712e-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-4" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_dd6663da55cf4169b3a8534c24258dfb" class="problems-wrapper" role="group" aria-labelledby="dd6663da55cf4169b3a8534c24258dfb-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;dd6663da55cf4169b3a8534c24258dfb-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART E &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@dd6663da55cf4169b3a8534c24258dfb-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;In the optimal solution, is a lockbox opened at Chicago?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_dd6663da55cf4169b3a8534c24258dfb_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_dd6663da55cf4169b3a8534c24258dfb_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_dd6663da55cf4169b3a8534c24258dfb_2_1&#34; id=&#34;input_dd6663da55cf4169b3a8534c24258dfb_2_1_choice_1a#B&#34; 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&lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_dd6663da55cf4169b3a8534c24258dfb_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_dd6663da55cf4169b3a8534c24258dfb_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART E&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_dd6663da55cf4169b3a8534c24258dfb&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; 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These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd6663da55cf4169b3a8534c24258dfb-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd6663da55cf4169b3a8534c24258dfb-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;dd6663da55cf4169b3a8534c24258dfb-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>

<div class="xblock xblock-public_view xblock-public_view-vertical" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@89c1dd87841e43c79dee304265a35149" data-block-type="vertical" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="False" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="VerticalStudentView" data-runtime-class="LmsRuntime" data-runtime-version="1"> <h2 class="hd hd-2 unit-title">Problem 5</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_9c420d0955d84fb9be59a57cd21f468e" class="problems-wrapper" role="group" aria-labelledby="9c420d0955d84fb9be59a57cd21f468e-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;9c420d0955d84fb9be59a57cd21f468e-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART A &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@9c420d0955d84fb9be59a57cd21f468e-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/72d138588e1ce7b4bb6a4c5deea59949/asset-v1:MITx+15.053x+3T2016+type@asset+block/revenuemap.png&#34;&gt; &lt;img width=&#34;550&#34; height=&#34;359&#34; alt=&#34;Map&#34; src=&#34;/assets/courseware/v1/72d138588e1ce7b4bb6a4c5deea59949/asset-v1:MITx+15.053x+3T2016+type@asset+block/revenuemap.png&#34;/&gt; &lt;/a&gt; &lt;/p&gt; &lt;p&gt;Airlines optimize their ticket sales in order to maximize their revenue. This is called the airline network revenue management problem. In this problem, we are trying to decide how many tickets for each origin-destination (O-D) pair to sell at each price level. The goal is to maximize revenue, and we cannot sell more tickets than there is demand for, or space on the planes for.&lt;/p&gt; &lt;p&gt;There are three origin-destination pairs, with two price classes for each pair. The three origin-destination pairs are BOS-MDW, MDW-SFO, or BOS-SFO via MDW. BOS stands for Boston, MDW is Chicago-Midway, and SFO is San Francisco. Each O-D pair has a &amp;#8220;regular&amp;#8221; and &amp;#8220;discount&amp;#8221; fare class. And there are two planes to serve the three origin-destination pairs. One plane flies from BOS to MDW, another plane flies from MDW to SFO. Each plane&amp;#8217;s capacity is 166 people. The data we will use is summarized as follows:&lt;/p&gt; &lt;div id=&#34;tb:1&#34; class=&#34;table&#34;&gt; &lt;center&gt; &lt;table cellspacing=&#34;0&#34; class=&#34;tabular&#34;&gt; &lt;tr&gt; &lt;td style=&#34;text-align:right; border-right:1px solid black&#34;&gt;&amp;#160;&lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Price &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;text-align:right&#34;&gt; &lt;p&gt; Demand &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; BOS-MDW Regular&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 428 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 80 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; BOS-MDW Discount&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 190 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 120 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; BOS-SFO Regular&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 642 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 75 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; BOS-SFO Discount&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 224 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 100 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; MDW-SFO Regular&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 512 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 60 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;tr&gt; &lt;td style=&#34;border-top-style:solid; text-align:right; border-top-color:black; border-top-width:1px; border-right:1px solid black&#34;&gt; &lt;p&gt; MDW-SFO Discount&lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 190 &lt;/p&gt; &lt;/td&gt; &lt;td style=&#34;border-top-style:solid; border-top-color:black; border-top-width:1px; text-align:right&#34;&gt; &lt;p&gt; 110 &lt;/p&gt; &lt;/td&gt; &lt;/tr&gt; &lt;/table&gt; &lt;div class=&#34;caption&#34;&gt; &lt;b&gt;Table 1: Fares for Origin-Destination (O-D) pairs&lt;/b&gt; &lt;span/&gt; &lt;/div&gt; &lt;label/&gt; &lt;/center&gt; &lt;/div&gt; &lt;p&gt; For this problem, we will make the (admittedly unrealistic) assumption that the demand for discount fairs and regular fairs is disjoint. For example, if we focus entirely on demand and not on airplane capacity, it is possible to sell 100 discount tickets from BOS to SFO and also sell 75 regular tickets from BOS to SFO. &lt;/p&gt; &lt;p&gt;Formulate an integer program that maximizes the total revenue. We can define decision vector \( x \) to refer to the number of tickets to sell for each O-D pair and fare class (i.e., \(x_{BOS-MDW-R}\) is the number of tickets to sell for O-D pair BOS-MDW with regular fare class, \(x_{BOS-MDW-D}\) is the number of tickets to sell for O-D pair BOS-MDW with discount fare class). Which of the following is the correct objective function for this maximization problem?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; id=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_0&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;9c420d0955d84fb9be59a57cd21f468e_2_1-choice_0-label&#34; for=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; \(618x_{BOS-MDW-R}+866x_{BOS-SFO-R}+702x_{MDW-SFO-R} \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; id=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_1&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;9c420d0955d84fb9be59a57cd21f468e_2_1-choice_1-label&#34; for=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; \(428x_{BOS-MDW-R}+642x_{BOS-SFO-R}+512x_{MDW-SFO-R} \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; id=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_2&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;9c420d0955d84fb9be59a57cd21f468e_2_1-choice_2-label&#34; for=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; \(80x_{BOS-MDW-R}+120x_{BOS-MDW-D}+75x_{BOS-SFO-R}+100x_{BOS-SFO-D}\\ +60x_{MDW-SFO-R} +110x_{MDW-SFO-D}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; id=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_3&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;9c420d0955d84fb9be59a57cd21f468e_2_1-choice_3-label&#34; for=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; \(428x_{BOS-MDW-R}+190x_{BOS-MDW-D}+642x_{BOS-SFO-R}+224x_{BOS-SFO-D}\\ +512x_{MDW-SFO-R} +190x_{MDW-SFO-D}\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; id=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_4&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;9c420d0955d84fb9be59a57cd21f468e_2_1-choice_4-label&#34; for=&#34;input_9c420d0955d84fb9be59a57cd21f468e_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;&gt; \(428x_{BOS-MDW-R}+80x_{BOS-MDW-R}+190x_{BOS-MDW-D}\\ +120x_{BOS-MDW-D}+512x_{BOS-SFO-R}+75x_{BOS-SFO-R}\\ +190x_{BOS-SFO-D}+100x_{BOS-SFO-D}+224x_{MDW-SFO-R}\\ +60x_{MDW-SFO-R}+190x_{MDW-SFO-D} +110x_{MDW-SFO-D}\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_9c420d0955d84fb9be59a57cd21f468e_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_9c420d0955d84fb9be59a57cd21f468e_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_9c420d0955d84fb9be59a57cd21f468e_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART A&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_9c420d0955d84fb9be59a57cd21f468e&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_9c420d0955d84fb9be59a57cd21f468e&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9c420d0955d84fb9be59a57cd21f468e-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9c420d0955d84fb9be59a57cd21f468e-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;9c420d0955d84fb9be59a57cd21f468e-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-1" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_2ea19ced87dc47d3bd9f414732e0e092" class="problems-wrapper" role="group" aria-labelledby="2ea19ced87dc47d3bd9f414732e0e092-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;2ea19ced87dc47d3bd9f414732e0e092-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART B &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@2ea19ced87dc47d3bd9f414732e0e092-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Choose the necessary constraint(s) (we cannot sell more tickets than there is demand for, or space on the planes for) from below. Select 5 sets of constraints.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_0&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_0&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_0-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_0&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-MDW-R} \leq 428, x_{BOS-MDW-D} \leq 190 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_1&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_1&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_1-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_1&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-SFO-R} \leq 642, x_{BOS-SFO-D} \leq 224 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_2&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_2&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_2-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_2&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{MDW-SFO-R} \leq 512, x_{MDW-SFO-D} \leq 190 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_3&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_3&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_3-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_3&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-MDW-R} \leq 80, x_{BOS-MDW-D} \leq 120 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_4&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_4&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_4-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_4&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-SFO-R} \leq 75, x_{BOS-SFO-D} \leq 100 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_5&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_5&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_5-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_5&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{MDW-SFO-R} \leq 60, x_{MDW-SFO-D} \leq 110 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_6&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_6&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_6-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_6&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-MDW-R} + x_{BOS-MDW-D} \leq 166 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_7&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_7&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_7-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_7&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{MDW-SFO-R}+ x_{MDW-SFO-D} \leq 166 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_8&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_8&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_8-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_8&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-SFO-R} + x_{BOS-SFO-D} \leq 166 \) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_9&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_9&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_9-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_9&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{BOS-MDW-R}+ x_{BOS-MDW-D}+x_{BOS-SFO-R}+x_{BOS-SFO-D} \leq 166\) &lt;/label&gt; &lt;/div&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;checkbox&#34; name=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1[]&#34; id=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_10&#34; class=&#34;field-input input-checkbox&#34; value=&#34;choice_10&#34;/&gt;&lt;label id=&#34;2ea19ced87dc47d3bd9f414732e0e092_2_1-choice_10-label&#34; for=&#34;input_2ea19ced87dc47d3bd9f414732e0e092_2_1_choice_10&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;&gt; \( x_{MDW-SFO-R}+ x_{MDW-SFO-D}+x_{BOS-SFO-R}+x_{BOS-SFO-D} \leq 166\) &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34;/&gt; &lt;/fieldset&gt; &lt;div class=&#34;indicator-container&#34;&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_2ea19ced87dc47d3bd9f414732e0e092_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;/div&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_2ea19ced87dc47d3bd9f414732e0e092_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART B&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_2ea19ced87dc47d3bd9f414732e0e092&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_2ea19ced87dc47d3bd9f414732e0e092&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2ea19ced87dc47d3bd9f414732e0e092-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2ea19ced87dc47d3bd9f414732e0e092-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;2ea19ced87dc47d3bd9f414732e0e092-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-2" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_e8073a189aa04ebab6fb5bf7fe8cc8ef" class="problems-wrapper" role="group" aria-labelledby="e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="3.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART C &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Solve this airline revenue management problemusing Julia and JuMP or Excel. What is the optimal total profit? Error checking hint. The optimal value is between 121000 and 121100.&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; id=&#34;input_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; data-input-id=&#34;e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_e8073a189aa04ebab6fb5bf7fe8cc8ef_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_e8073a189aa04ebab6fb5bf7fe8cc8ef_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART C&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_e8073a189aa04ebab6fb5bf7fe8cc8ef&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_e8073a189aa04ebab6fb5bf7fe8cc8ef&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;e8073a189aa04ebab6fb5bf7fe8cc8ef-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> <div class="vert vert-3" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583" data-block-type="problem" data-graded="True" data-course-id="course-v1:MITx+15.053x+3T2016" data-has-score="True" data-request-token="5593f363852711ef8f57023e4242adeb" data-init="XBlockToXModuleShim" data-runtime-class="LmsRuntime" data-runtime-version="1"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_14c51b1880534f78858ade194e911583" class="problems-wrapper" role="group" aria-labelledby="14c51b1880534f78858ade194e911583-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583/handler/xmodule_handler" data-problem-score="0.0" data-problem-total-possible="1.0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;14c51b1880534f78858ade194e911583-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583-problem-progress&#34; tabindex=&#34;-1&#34;&gt; PART D &lt;/h3&gt; &lt;div class=&#34;problem-progress&#34; id=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@14c51b1880534f78858ade194e911583-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;How many discount MDW to SFO seats should be sold?&lt;/p&gt; &lt;div class=&#34;wrapper-problem-response&#34; tabindex=&#34;-1&#34; aria-label=&#34;Question 1&#34; role=&#34;group&#34;&gt;&lt;div id=&#34;formulaequationinput_14c51b1880534f78858ade194e911583_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;input type=&#34;text&#34; name=&#34;input_14c51b1880534f78858ade194e911583_2_1&#34; id=&#34;input_14c51b1880534f78858ade194e911583_2_1&#34; data-input-id=&#34;14c51b1880534f78858ade194e911583_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_14c51b1880534f78858ade194e911583_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_14c51b1880534f78858ade194e911583_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_14c51b1880534f78858ade194e911583_2_1&#34; data-tooltip=&#34;Not yet answered.&#34;&gt; &lt;span class=&#34;sr&#34;&gt;unanswered&lt;/span&gt;&lt;span class=&#34;status-icon&#34; aria-hidden=&#34;true&#34;/&gt; &lt;/span&gt; &lt;p id=&#34;answer_14c51b1880534f78858ade194e911583_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_14c51b1880534f78858ade194e911583_2_1_preview&#34; class=&#34;equation&#34;&gt; \(\) &lt;img src=&#34;/static/images/spinner.bc34f953403f.gif&#34; class=&#34;loading&#34; alt=&#34;Loading&#34;/&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;script_placeholder&#34; data-src=&#34;/static/js/capa/src/formula_equation_preview.b1967ab28c31.js&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;solution-span&#34;&gt; &lt;span id=&#34;solution_14c51b1880534f78858ade194e911583_solution_1&#34;/&gt; &lt;/div&gt;&lt;/div&gt; &lt;div class=&#34;action&#34;&gt; &lt;input type=&#34;hidden&#34; name=&#34;problem_id&#34; value=&#34;PART D&#34; /&gt; &lt;div class=&#34;submit-attempt-container&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;submit btn-brand&#34; data-submitting=&#34;Submitting&#34; data-value=&#34;Submit&#34; data-should-enable-submit-button=&#34;True&#34; aria-describedby=&#34;submission_feedback_14c51b1880534f78858ade194e911583&#34; &gt; &lt;span class=&#34;submit-label&#34;&gt;Submit&lt;/span&gt; &lt;/button&gt; &lt;div class=&#34;submission-feedback&#34; id=&#34;submission_feedback_14c51b1880534f78858ade194e911583&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.&lt;/span&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;problem-action-buttons-wrapper&#34;&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-gentle-alert is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-exclamation-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;14c51b1880534f78858ade194e911583-problem-title&#34;&gt; &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification warning notification-save is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-save&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;14c51b1880534f78858ade194e911583-problem-title&#34;&gt;None &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;div class=&#34;notification general notification-show-answer is-hidden&#34; tabindex=&#34;-1&#34;&gt; &lt;span class=&#34;icon fa fa-info-circle&#34; aria-hidden=&#34;true&#34;&gt;&lt;/span&gt; &lt;span class=&#34;notification-message&#34; aria-describedby=&#34;14c51b1880534f78858ade194e911583-problem-title&#34;&gt;Answers are displayed within the problem &lt;/span&gt; &lt;div class=&#34;notification-btn-wrapper&#34;&gt; &lt;button type=&#34;button&#34; class=&#34;btn btn-default btn-small notification-btn review-btn sr&#34;&gt;Review&lt;/button&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt; " data-graded="True"> <p class="loading-spinner"> <i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i> <span class="sr">Loading&hellip;</span> </p> </div> </div> </div> </div> </div>