<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="False" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@51dd730695884296b2e08e1855f369ad" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Practice Problem 1</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6aaeee3ac7154f16890da83acd1f33d2"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6aaeee3ac7154f16890da83acd1f33d2" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_6aaeee3ac7154f16890da83acd1f33d2" class="problems-wrapper" role="group" aria-labelledby="6aaeee3ac7154f16890da83acd1f33d2-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@6aaeee3ac7154f16890da83acd1f33d2" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@6aaeee3ac7154f16890da83acd1f33d2/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;6aaeee3ac7154f16890da83acd1f33d2-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@6aaeee3ac7154f16890da83acd1f33d2-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@6aaeee3ac7154f16890da83acd1f33d2-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;(Excerpted from Applied Mathematical Programming (AMP), Chapter 9, exercise 3).&lt;/p&gt; &lt;p&gt;Note to students. The following problem was written in 1977. The same problem is applicable today, except that it would include other forms of advertising, including Google and Facebook and other social media. &lt;/p&gt; &lt;p&gt;The marketing group of A. J. Pitt Company is considering the options available for its next advertising campaign program. After a great deal of work, the group has identified a selected number of options with the characteristics shown in the accompanying table.&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;TV&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Trade Magazine&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Newspaper&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Radio&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Popular magazine&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Promotional campaign&lt;/th&gt; &lt;th scope=&#34;col&#34; style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;Total resource available&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;Customers reached&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;1,000,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;200,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;300,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;400,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;450,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;450,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;-&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;Cost ($)&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;500,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;150,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;300,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;250,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;250,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;100,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;1,800,000&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;Designers needed (man-hours)&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;700&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;250&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;200&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;200&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;300&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;400&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;1,500&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;Salesmen needed (man-hours)&lt;/th&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;200&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;100&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;100&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;100&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;100&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;1,000&lt;/td&gt; &lt;td style=&#34;text-align: center; border: 1px solid black; padding: 10px;&#34;&gt;1,200&lt;/td&gt; &lt;/tr&gt; &lt;/tbody&gt; &lt;caption&gt;Table 1: Advertising Campaign Options&lt;/caption&gt; &lt;/table&gt; &lt;/center&gt; &lt;p&gt;The objective of the advertising program is to maximize the number of customers reached, subject to the limitation of resources (money, designers, and salesman) given in the table above. In addition, the following constraints have to be met:&lt;/p&gt; &lt;ul&gt; &lt;li&gt;If the promotional campaign is undertaken, it needs either a radio or a popular magazine campaign effort to support it.&lt;/li&gt; &lt;li&gt;The firm cannot advertise in both the trade and popular magazines.&lt;/li&gt; &lt;/ul&gt; &lt;p&gt;Formulate an integer-programming model that will assist the company to select an appropriate advertising campaign strategy. &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_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;label class=&#34;problem-group-label&#34; for=&#34;input_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; id=&#34;label_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34;&gt;How many binary decision variables are in your integer program?&lt;/label&gt; &lt;input type=&#34;text&#34; name=&#34;input_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; id=&#34;input_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; data-input-id=&#34;6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_6aaeee3ac7154f16890da83acd1f33d2_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_6aaeee3ac7154f16890da83acd1f33d2_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_6aaeee3ac7154f16890da83acd1f33d2_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_6aaeee3ac7154f16890da83acd1f33d2_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_6aaeee3ac7154f16890da83acd1f33d2&#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_6aaeee3ac7154f16890da83acd1f33d2&#34;&gt; &lt;span class=&#34;sr&#34;&gt;Some problems have options such as save, reset, hints, or show answer. 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id=&#34;427077aedd8541c3b51c813edb915afd-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@427077aedd8541c3b51c813edb915afd-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@427077aedd8541c3b51c813edb915afd-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;How many constraints are in your integer program, other than the constraints that a variable is binary?&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_427077aedd8541c3b51c813edb915afd_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_427077aedd8541c3b51c813edb915afd_2_1&#34; id=&#34;input_427077aedd8541c3b51c813edb915afd_2_1&#34; 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&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;427077aedd8541c3b51c813edb915afd-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="False"> <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@4e9d12d2527b427bb9fce677b79aff8d"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4e9d12d2527b427bb9fce677b79aff8d" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_4e9d12d2527b427bb9fce677b79aff8d" class="problems-wrapper" role="group" aria-labelledby="4e9d12d2527b427bb9fce677b79aff8d-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@4e9d12d2527b427bb9fce677b79aff8d" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@4e9d12d2527b427bb9fce677b79aff8d/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;4e9d12d2527b427bb9fce677b79aff8d-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@4e9d12d2527b427bb9fce677b79aff8d-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@4e9d12d2527b427bb9fce677b79aff8d-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; If you want the option of showing our integer programming formulation, click below. &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_4e9d12d2527b427bb9fce677b79aff8d_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_4e9d12d2527b427bb9fce677b79aff8d_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_4e9d12d2527b427bb9fce677b79aff8d_2_1&#34; id=&#34;input_4e9d12d2527b427bb9fce677b79aff8d_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;4e9d12d2527b427bb9fce677b79aff8d_2_1-choice_3eaA-label&#34; for=&#34;input_4e9d12d2527b427bb9fce677b79aff8d_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_4e9d12d2527b427bb9fce677b79aff8d_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_4e9d12d2527b427bb9fce677b79aff8d_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_4e9d12d2527b427bb9fce677b79aff8d_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_4e9d12d2527b427bb9fce677b79aff8d_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_4e9d12d2527b427bb9fce677b79aff8d&#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_4e9d12d2527b427bb9fce677b79aff8d&#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;4e9d12d2527b427bb9fce677b79aff8d-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;4e9d12d2527b427bb9fce677b79aff8d-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;4e9d12d2527b427bb9fce677b79aff8d-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="False"> <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@df2a8c978585499791193b26980f13aa"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@df2a8c978585499791193b26980f13aa" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_df2a8c978585499791193b26980f13aa" class="problems-wrapper" role="group" aria-labelledby="df2a8c978585499791193b26980f13aa-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@df2a8c978585499791193b26980f13aa" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@df2a8c978585499791193b26980f13aa/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;df2a8c978585499791193b26980f13aa-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@df2a8c978585499791193b26980f13aa-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@df2a8c978585499791193b26980f13aa-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Model the advertising problem using Excel and solve it using Solver or OpenSolver. An initial spreadsheet containing the data is &lt;a class=&#34;modal-content&#34; href=&#34;/assets/courseware/v1/39926167f2e960a35dcb8421411c7d6b/asset-v1:MITx+15.053x+3T2016+type@asset+block/R4P1Data.csv&#34;&gt; here&lt;/a&gt;, with the headers and columns already removed. &lt;/p&gt; &lt;p&gt;Or model the advertising problem using Julia and JuMP, starting with the data in the spreadsheet&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_df2a8c978585499791193b26980f13aa_2_1&#34; class=&#34;inputtype formulaequationinput&#34;&gt; &lt;div class=&#34;unanswered&#34;&gt; &lt;label class=&#34;problem-group-label&#34; for=&#34;input_df2a8c978585499791193b26980f13aa_2_1&#34; id=&#34;label_df2a8c978585499791193b26980f13aa_2_1&#34;&gt;What is the optimal objective value?&lt;/label&gt; &lt;input type=&#34;text&#34; name=&#34;input_df2a8c978585499791193b26980f13aa_2_1&#34; id=&#34;input_df2a8c978585499791193b26980f13aa_2_1&#34; data-input-id=&#34;df2a8c978585499791193b26980f13aa_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_df2a8c978585499791193b26980f13aa_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_df2a8c978585499791193b26980f13aa_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_df2a8c978585499791193b26980f13aa_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_df2a8c978585499791193b26980f13aa_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_df2a8c978585499791193b26980f13aa_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_df2a8c978585499791193b26980f13aa_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_df2a8c978585499791193b26980f13aa&#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_df2a8c978585499791193b26980f13aa&#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;df2a8c978585499791193b26980f13aa-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;df2a8c978585499791193b26980f13aa-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;df2a8c978585499791193b26980f13aa-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="False"> <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-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="False" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@1ea47924820f46609dbfeb64c9e44610" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Practice Problem 2</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@3a9327f2bab54d94b9a0d03e6e8aa4c3"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@3a9327f2bab54d94b9a0d03e6e8aa4c3" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_3a9327f2bab54d94b9a0d03e6e8aa4c3" class="problems-wrapper" role="group" aria-labelledby="3a9327f2bab54d94b9a0d03e6e8aa4c3-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@3a9327f2bab54d94b9a0d03e6e8aa4c3" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@3a9327f2bab54d94b9a0d03e6e8aa4c3/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;3a9327f2bab54d94b9a0d03e6e8aa4c3-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@3a9327f2bab54d94b9a0d03e6e8aa4c3-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@3a9327f2bab54d94b9a0d03e6e8aa4c3-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt; Three different items are to be routed through three machines. Each item must be processed first on machine 1, then on machine 2, and finally on machine 3. The sequence of items may differ for each machine. Assume that the times \(t_{ij}\) required to perform the work on item \(i\) by machine \(j\) are known and are integers. Our objective is to minimize the total time necessary to process all the items. In PARTS A to E, we will formulate the problem as an integer program. (All of the parts are put together in PART F.)&lt;/p&gt; &lt;p&gt;Let \( x_{ij} \) denote the time at which job \( i \) starts being processed on machine \( j \). The objective is to minimize z, which is the first time at which all of the jobs are completed. What additional constraints are needed to ensure that z is the earliest time at which all jobs are completed? When you are ready to have the answer shown, click 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_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1&#34; id=&#34;input_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1-choice_3eaA-label&#34; for=&#34;input_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_3a9327f2bab54d94b9a0d03e6e8aa4c3_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_3a9327f2bab54d94b9a0d03e6e8aa4c3_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_3a9327f2bab54d94b9a0d03e6e8aa4c3_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_3a9327f2bab54d94b9a0d03e6e8aa4c3_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_3a9327f2bab54d94b9a0d03e6e8aa4c3&#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_3a9327f2bab54d94b9a0d03e6e8aa4c3&#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;3a9327f2bab54d94b9a0d03e6e8aa4c3-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;3a9327f2bab54d94b9a0d03e6e8aa4c3-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;3a9327f2bab54d94b9a0d03e6e8aa4c3-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="False"> <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@87d966d500b944ba89911eb73b791093"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@87d966d500b944ba89911eb73b791093" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_87d966d500b944ba89911eb73b791093" class="problems-wrapper" role="group" aria-labelledby="87d966d500b944ba89911eb73b791093-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@87d966d500b944ba89911eb73b791093" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@87d966d500b944ba89911eb73b791093/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;87d966d500b944ba89911eb73b791093-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@87d966d500b944ba89911eb73b791093-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@87d966d500b944ba89911eb73b791093-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Write the constraints that ensure that jobs 1 and 2 do not overlap when scheduled on Machine 1. When you are ready to have the answer shown, click below. &lt;/p&gt; &lt;p&gt; &lt;i&gt;HINT: you will need to use the big M method.&lt;/i&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 class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_87d966d500b944ba89911eb73b791093_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_87d966d500b944ba89911eb73b791093_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_87d966d500b944ba89911eb73b791093_2_1&#34; id=&#34;input_87d966d500b944ba89911eb73b791093_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;87d966d500b944ba89911eb73b791093_2_1-choice_3eaA-label&#34; for=&#34;input_87d966d500b944ba89911eb73b791093_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_87d966d500b944ba89911eb73b791093_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_87d966d500b944ba89911eb73b791093_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_87d966d500b944ba89911eb73b791093_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_87d966d500b944ba89911eb73b791093_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_87d966d500b944ba89911eb73b791093&#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_87d966d500b944ba89911eb73b791093&#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;87d966d500b944ba89911eb73b791093-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;87d966d500b944ba89911eb73b791093-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;87d966d500b944ba89911eb73b791093-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="False"> <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@637ff66ba64a42aa9e755bebc7dab865"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@637ff66ba64a42aa9e755bebc7dab865" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_637ff66ba64a42aa9e755bebc7dab865" class="problems-wrapper" role="group" aria-labelledby="637ff66ba64a42aa9e755bebc7dab865-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@637ff66ba64a42aa9e755bebc7dab865" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@637ff66ba64a42aa9e755bebc7dab865/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;637ff66ba64a42aa9e755bebc7dab865-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@637ff66ba64a42aa9e755bebc7dab865-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@637ff66ba64a42aa9e755bebc7dab865-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Write the constraints that ensure that no two of the jobs overlap when scheduled on any of the three machines. When you are ready to have the answer shown, click 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_637ff66ba64a42aa9e755bebc7dab865_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_637ff66ba64a42aa9e755bebc7dab865_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_637ff66ba64a42aa9e755bebc7dab865_2_1&#34; id=&#34;input_637ff66ba64a42aa9e755bebc7dab865_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;637ff66ba64a42aa9e755bebc7dab865_2_1-choice_3eaA-label&#34; for=&#34;input_637ff66ba64a42aa9e755bebc7dab865_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_637ff66ba64a42aa9e755bebc7dab865_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_637ff66ba64a42aa9e755bebc7dab865_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_637ff66ba64a42aa9e755bebc7dab865_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_637ff66ba64a42aa9e755bebc7dab865_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_637ff66ba64a42aa9e755bebc7dab865&#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_637ff66ba64a42aa9e755bebc7dab865&#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;637ff66ba64a42aa9e755bebc7dab865-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;637ff66ba64a42aa9e755bebc7dab865-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;637ff66ba64a42aa9e755bebc7dab865-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="False"> <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@78d3aabe09c8453e9368b97906457a39"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@78d3aabe09c8453e9368b97906457a39" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_78d3aabe09c8453e9368b97906457a39" class="problems-wrapper" role="group" aria-labelledby="78d3aabe09c8453e9368b97906457a39-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@78d3aabe09c8453e9368b97906457a39" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@78d3aabe09c8453e9368b97906457a39/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;78d3aabe09c8453e9368b97906457a39-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@78d3aabe09c8453e9368b97906457a39-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@78d3aabe09c8453e9368b97906457a39-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Write the constraint that ensures that the time that job 1 runs on Machine 2 is at least equal to the time that it completes on Machine 1. &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_78d3aabe09c8453e9368b97906457a39_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_78d3aabe09c8453e9368b97906457a39_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_78d3aabe09c8453e9368b97906457a39_2_1&#34; id=&#34;input_78d3aabe09c8453e9368b97906457a39_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;78d3aabe09c8453e9368b97906457a39_2_1-choice_3eaA-label&#34; for=&#34;input_78d3aabe09c8453e9368b97906457a39_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_78d3aabe09c8453e9368b97906457a39_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_78d3aabe09c8453e9368b97906457a39_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_78d3aabe09c8453e9368b97906457a39_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_78d3aabe09c8453e9368b97906457a39_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_78d3aabe09c8453e9368b97906457a39&#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_78d3aabe09c8453e9368b97906457a39&#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;78d3aabe09c8453e9368b97906457a39-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;78d3aabe09c8453e9368b97906457a39-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;78d3aabe09c8453e9368b97906457a39-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="False"> <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@14da31e82b4d4c5899cc583944d2977f"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@14da31e82b4d4c5899cc583944d2977f" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_14da31e82b4d4c5899cc583944d2977f" class="problems-wrapper" role="group" aria-labelledby="14da31e82b4d4c5899cc583944d2977f-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@14da31e82b4d4c5899cc583944d2977f" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@14da31e82b4d4c5899cc583944d2977f/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;14da31e82b4d4c5899cc583944d2977f-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@14da31e82b4d4c5899cc583944d2977f-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@14da31e82b4d4c5899cc583944d2977f-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Write the constraints that ensure that the time that job i runs on Machine j is at least equal to the time that it completes on Machine \(j-1\) for all \(i = 1\) to 3 and \(j = 2 \) to 3. &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_14da31e82b4d4c5899cc583944d2977f_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_14da31e82b4d4c5899cc583944d2977f_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_14da31e82b4d4c5899cc583944d2977f_2_1&#34; id=&#34;input_14da31e82b4d4c5899cc583944d2977f_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;14da31e82b4d4c5899cc583944d2977f_2_1-choice_3eaA-label&#34; for=&#34;input_14da31e82b4d4c5899cc583944d2977f_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_14da31e82b4d4c5899cc583944d2977f_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_14da31e82b4d4c5899cc583944d2977f_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_14da31e82b4d4c5899cc583944d2977f_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_14da31e82b4d4c5899cc583944d2977f_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_14da31e82b4d4c5899cc583944d2977f&#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_14da31e82b4d4c5899cc583944d2977f&#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;14da31e82b4d4c5899cc583944d2977f-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;14da31e82b4d4c5899cc583944d2977f-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;14da31e82b4d4c5899cc583944d2977f-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="False"> <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@f18d6a347c1846f59d66ec4d6df0bba0"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@f18d6a347c1846f59d66ec4d6df0bba0" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_f18d6a347c1846f59d66ec4d6df0bba0" class="problems-wrapper" role="group" aria-labelledby="f18d6a347c1846f59d66ec4d6df0bba0-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@f18d6a347c1846f59d66ec4d6df0bba0" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@f18d6a347c1846f59d66ec4d6df0bba0/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;f18d6a347c1846f59d66ec4d6df0bba0-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@f18d6a347c1846f59d66ec4d6df0bba0-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@f18d6a347c1846f59d66ec4d6df0bba0-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Are you ready to see the entire formulation? &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_f18d6a347c1846f59d66ec4d6df0bba0_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_f18d6a347c1846f59d66ec4d6df0bba0_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_f18d6a347c1846f59d66ec4d6df0bba0_2_1&#34; id=&#34;input_f18d6a347c1846f59d66ec4d6df0bba0_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;f18d6a347c1846f59d66ec4d6df0bba0_2_1-choice_3eaA-label&#34; for=&#34;input_f18d6a347c1846f59d66ec4d6df0bba0_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_f18d6a347c1846f59d66ec4d6df0bba0_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_f18d6a347c1846f59d66ec4d6df0bba0_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_f18d6a347c1846f59d66ec4d6df0bba0_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_f18d6a347c1846f59d66ec4d6df0bba0_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_f18d6a347c1846f59d66ec4d6df0bba0&#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_f18d6a347c1846f59d66ec4d6df0bba0&#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;f18d6a347c1846f59d66ec4d6df0bba0-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;f18d6a347c1846f59d66ec4d6df0bba0-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;f18d6a347c1846f59d66ec4d6df0bba0-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="False"> <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-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="False" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@vertical+block@d106d0ea8f1946b6ad2ea2a4f602b809" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="VerticalStudentView" data-graded="False" data-block-type="vertical"> <h2 class="hd hd-2 unit-title">Practice Problem 3</h2> <div class="vert-mod"> <div class="vert vert-0" data-id="block-v1:MITx+15.053x+3T2016+type@problem+block@85d862305ab84c55addd158f2d09f645"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@85d862305ab84c55addd158f2d09f645" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_85d862305ab84c55addd158f2d09f645" class="problems-wrapper" role="group" aria-labelledby="85d862305ab84c55addd158f2d09f645-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@85d862305ab84c55addd158f2d09f645" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@85d862305ab84c55addd158f2d09f645/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;85d862305ab84c55addd158f2d09f645-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@85d862305ab84c55addd158f2d09f645-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@85d862305ab84c55addd158f2d09f645-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Consider the problem:&lt;/p&gt; &lt;p class=&#34;equation&#34;&gt;\[\left.\begin{array}{rrcl} \max &amp;amp; x_1 + x_2 \\ \text {s.t.:} &amp;amp; &amp;amp; &amp;amp; \\ &amp;amp; x_1 + x_2 \leq 8 \\ &amp;amp; -x_1 +x_2 \leq 2 \\ &amp;amp; x_1 - x_2 \leq 4 \\ &amp;amp; x_2 \geq 0 \\ &amp;amp; x_1 \in \{0,1,4,6 \} \end{array}\right\}\]&lt;/p&gt; &lt;p&gt;When you formulate this problem as an IP, how many binary variables need to be added (Assume that no non-binary variables are added)?&lt;/p&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_85d862305ab84c55addd158f2d09f645_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_85d862305ab84c55addd158f2d09f645_2_1&#34; id=&#34;input_85d862305ab84c55addd158f2d09f645_2_1&#34; data-input-id=&#34;85d862305ab84c55addd158f2d09f645_2_1&#34; value=&#34;&#34; aria-describedby=&#34;status_85d862305ab84c55addd158f2d09f645_2_1&#34; size=&#34;20&#34;/&gt; &lt;span class=&#34;trailing_text&#34; id=&#34;trailing_text_85d862305ab84c55addd158f2d09f645_2_1&#34;/&gt; &lt;span class=&#34;status unanswered&#34; id=&#34;status_85d862305ab84c55addd158f2d09f645_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_85d862305ab84c55addd158f2d09f645_2_1&#34; class=&#34;answer&#34;/&gt; &lt;div id=&#34;input_85d862305ab84c55addd158f2d09f645_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_85d862305ab84c55addd158f2d09f645_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_85d862305ab84c55addd158f2d09f645&#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_85d862305ab84c55addd158f2d09f645&#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;85d862305ab84c55addd158f2d09f645-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;85d862305ab84c55addd158f2d09f645-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;85d862305ab84c55addd158f2d09f645-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="False"> <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@badf97ae3bad4d36a18d0479e4f2253c"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@badf97ae3bad4d36a18d0479e4f2253c" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_badf97ae3bad4d36a18d0479e4f2253c" class="problems-wrapper" role="group" aria-labelledby="badf97ae3bad4d36a18d0479e4f2253c-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@badf97ae3bad4d36a18d0479e4f2253c" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@badf97ae3bad4d36a18d0479e4f2253c/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;badf97ae3bad4d36a18d0479e4f2253c-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@badf97ae3bad4d36a18d0479e4f2253c-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@badf97ae3bad4d36a18d0479e4f2253c-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;Formulate the problem as an equivalent integer program&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_badf97ae3bad4d36a18d0479e4f2253c_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_badf97ae3bad4d36a18d0479e4f2253c_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_badf97ae3bad4d36a18d0479e4f2253c_2_1&#34; id=&#34;input_badf97ae3bad4d36a18d0479e4f2253c_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;badf97ae3bad4d36a18d0479e4f2253c_2_1-choice_3eaA-label&#34; for=&#34;input_badf97ae3bad4d36a18d0479e4f2253c_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_badf97ae3bad4d36a18d0479e4f2253c_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_badf97ae3bad4d36a18d0479e4f2253c_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_badf97ae3bad4d36a18d0479e4f2253c_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_badf97ae3bad4d36a18d0479e4f2253c_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_badf97ae3bad4d36a18d0479e4f2253c&#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_badf97ae3bad4d36a18d0479e4f2253c&#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;badf97ae3bad4d36a18d0479e4f2253c-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;badf97ae3bad4d36a18d0479e4f2253c-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;badf97ae3bad4d36a18d0479e4f2253c-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="False"> <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@36702371858a4eecadc718df032dd5c4"> <div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="de2f4b825b0611ee8f4f162ded714679" data-has-score="True" data-runtime-version="1" data-usage-id="block-v1:MITx+15.053x+3T2016+type@problem+block@36702371858a4eecadc718df032dd5c4" data-course-id="course-v1:MITx+15.053x+3T2016" data-runtime-class="LmsRuntime" data-init="XBlockToXModuleShim" data-graded="False" data-block-type="problem"> <script type="json/xblock-args" class="xblock-json-init-args"> {"xmodule-type": "Problem"} </script> <div id="problem_36702371858a4eecadc718df032dd5c4" class="problems-wrapper" role="group" aria-labelledby="36702371858a4eecadc718df032dd5c4-problem-title" data-problem-id="block-v1:MITx+15.053x+3T2016+type@problem+block@36702371858a4eecadc718df032dd5c4" data-url="/courses/course-v1:MITx+15.053x+3T2016/xblock/block-v1:MITx+15.053x+3T2016+type@problem+block@36702371858a4eecadc718df032dd5c4/handler/xmodule_handler" data-problem-score="0" data-problem-total-possible="0" data-attempts-used="0" data-content=" &lt;h3 class=&#34;hd hd-3 problem-header&#34; id=&#34;36702371858a4eecadc718df032dd5c4-problem-title&#34; aria-describedby=&#34;block-v1:MITx+15.053x+3T2016+type@problem+block@36702371858a4eecadc718df032dd5c4-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@36702371858a4eecadc718df032dd5c4-problem-progress&#34;&gt;&lt;/div&gt; &lt;div class=&#34;problem&#34;&gt; &lt;div&gt; &lt;p&gt;How would your answer to the previous part change if the objective function were changed to:&lt;/p&gt; &lt;p&gt;\[\text{ MAX } x_1^2 +2x_2\]&lt;/p&gt; &lt;p&gt; &lt;i&gt;NOTE: It is possible to modify the problem in many different ways. See if you can find a way that adds a single decision variable \(y\) (which will be equal to \((x_1)^2\)) and only one additional constraint.&lt;/i&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 class=&#34;choicegroup capa_inputtype&#34; id=&#34;inputtype_36702371858a4eecadc718df032dd5c4_2_1&#34;&gt; &lt;fieldset aria-describedby=&#34;status_36702371858a4eecadc718df032dd5c4_2_1&#34;&gt; &lt;div class=&#34;field&#34;&gt; &lt;input type=&#34;radio&#34; name=&#34;input_36702371858a4eecadc718df032dd5c4_2_1&#34; id=&#34;input_36702371858a4eecadc718df032dd5c4_2_1_choice_3eaA&#34; class=&#34;field-input input-radio&#34; value=&#34;choice_3eaA&#34;/&gt;&lt;label id=&#34;36702371858a4eecadc718df032dd5c4_2_1-choice_3eaA-label&#34; for=&#34;input_36702371858a4eecadc718df032dd5c4_2_1_choice_3eaA&#34; class=&#34;response-label field-label label-inline&#34; aria-describedby=&#34;status_36702371858a4eecadc718df032dd5c4_2_1&#34;&gt; I am ready to have the answer shown &lt;/label&gt; &lt;/div&gt; &lt;span id=&#34;answer_36702371858a4eecadc718df032dd5c4_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_36702371858a4eecadc718df032dd5c4_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_36702371858a4eecadc718df032dd5c4_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_36702371858a4eecadc718df032dd5c4&#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_36702371858a4eecadc718df032dd5c4&#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;36702371858a4eecadc718df032dd5c4-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;36702371858a4eecadc718df032dd5c4-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;36702371858a4eecadc718df032dd5c4-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="False"> <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>