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<h2 class="hd hd-2 unit-title">Slides</h2>
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<p><i>Slides available <a class="modal-content" href="/assets/courseware/v1/c0c23f89c413183c473db185ed6c928f/asset-v1:MITx+15.053x+3T2016+type@asset+block/Week_5_slides.pdf"> here</a></i> </p>
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<h2 class="hd hd-2 unit-title">Overview</h2>
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<h2 class="hd hd-2 unit-title">Geometry Overview</h2>
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<h3 class="hd hd-2">Geometry Overview</h3>
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<h2 class="hd hd-2 unit-title">Geometry Exercise</h2>
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PART A
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<p>The objective function is \("3R + 2G."\) Suppose that the objective function is changed to \(3.001 R + 2.001 G\). Which of the following is true:</p>
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The optimal objective value stays the same
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The optimal objective value decreases
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PART B
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<p>The first constraint is \(R + G &#8804; 8.\) Suppose it is changed to \(R + G &#8804; 7.9\). Which of the following is true:</p>
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The optimal solution stays the same.
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The optimal objective value stays the same
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The optimal objective value decreases
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<h2 class="hd hd-2 unit-title">Cost Coefficient 1</h2>
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<h2 class="hd hd-2 unit-title">Cost Coefficient 2</h2>
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<h2 class="hd hd-2 unit-title">Cost Coefficient 2 Exercise</h2>
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Cost Coefficient 2 Exercise
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<p>Suppose that there is a unique optimal solution \((x^*, y^*) \) and the cost coefficients are modified, perhaps by more than a little bit. Which of the following can happen?&#8221; Select all that are possible</p>
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The solution \((x^*, y^*) \) remains a unique optimal solution
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The solution \((x^*, y^*) \) remains optimal, but there are multiple optimal solutions
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A solution other than \((x^*, y^*) \) is the unique optimal solution
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There is no feasible solution
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<h2 class="hd hd-2 unit-title">Shadow Price 1 Exercise</h2>
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PART A
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<p>Consider the R/G widget problem.</p>
<p>Recall that the optimal objective value is 21, and there is a constraint \(R + G \leq 8\). Suppose we change the RHS of the constraint from 8 to 6. What is the new objective value? You may need to review the sensitivity report in the video.</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
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<input type="radio" name="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1" id="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="1f0862eeedc14a8b9dd5194f43f4b13b_2_1-choice_0-label" for="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
\(
17
\)
</label>
</div>
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<input type="radio" name="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1" id="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="1f0862eeedc14a8b9dd5194f43f4b13b_2_1-choice_1-label" for="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
\(
19
\)
</label>
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<input type="radio" name="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1" id="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="1f0862eeedc14a8b9dd5194f43f4b13b_2_1-choice_2-label" for="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
\(
21
\)
</label>
</div>
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<input type="radio" name="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1" id="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="1f0862eeedc14a8b9dd5194f43f4b13b_2_1-choice_3-label" for="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
\(
23
\)
</label>
</div>
<div class="field">
<input type="radio" name="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1" id="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="1f0862eeedc14a8b9dd5194f43f4b13b_2_1-choice_4-label" for="input_1f0862eeedc14a8b9dd5194f43f4b13b_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_1f0862eeedc14a8b9dd5194f43f4b13b_2_1">
\(
25
\)
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PART B
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<p>Suppose we further restrict the sum to 5. What is the new objective value? You may need to review the sensitivity report in the video.</p>
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Not enough information
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<div class="field">
<input type="radio" name="input_51820cdf37354413bf566081d8ab3994_2_1" id="input_51820cdf37354413bf566081d8ab3994_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="51820cdf37354413bf566081d8ab3994_2_1-choice_1-label" for="input_51820cdf37354413bf566081d8ab3994_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_51820cdf37354413bf566081d8ab3994_2_1">
\(
15
\)
</label>
</div>
<div class="field">
<input type="radio" name="input_51820cdf37354413bf566081d8ab3994_2_1" id="input_51820cdf37354413bf566081d8ab3994_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="51820cdf37354413bf566081d8ab3994_2_1-choice_2-label" for="input_51820cdf37354413bf566081d8ab3994_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_51820cdf37354413bf566081d8ab3994_2_1">
\(
17
\)
</label>
</div>
<div class="field">
<input type="radio" name="input_51820cdf37354413bf566081d8ab3994_2_1" id="input_51820cdf37354413bf566081d8ab3994_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="51820cdf37354413bf566081d8ab3994_2_1-choice_3-label" for="input_51820cdf37354413bf566081d8ab3994_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_51820cdf37354413bf566081d8ab3994_2_1">
\(
18
\)
</label>
</div>
<div class="field">
<input type="radio" name="input_51820cdf37354413bf566081d8ab3994_2_1" id="input_51820cdf37354413bf566081d8ab3994_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="51820cdf37354413bf566081d8ab3994_2_1-choice_4-label" for="input_51820cdf37354413bf566081d8ab3994_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_51820cdf37354413bf566081d8ab3994_2_1">
\(
21
\)
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<h2 class="hd hd-2 unit-title">Shadow Price 2</h2>
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<h2 class="hd hd-2 unit-title">AMP Example</h2>
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<h2 class="hd hd-2 unit-title">Changing Coefficients 1</h2>
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<h2 class="hd hd-2 unit-title">Changing Coefficients Exercise 1</h2>
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Changing Coefficients Exercise 1
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<p> Suppose that the objective function is changed to \( 3 G + 10 R \). Will the optimal solution change?</p>
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<h2 class="hd hd-2 unit-title">Changing Coefficients 2</h2>
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<h2 class="hd hd-2 unit-title">Changing Coefficients 2 Exercise</h2>
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Changing Coefficients 2 Exercise
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<p> Suppose that the amount of production capacity increased from 60 to 62 to and the amount of warehouse capacity increased from 150 to 165. What is the increase in the optimal objective value? Answer "-1" if there is not enough information to determine the correct answer. </p>
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<h2 class="hd hd-2 unit-title">Pricing Out 2 Exercise</h2>
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Pricing Out 2 Exercise
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<p>Consider the glass problem, with the following adjustment. Suppose instead that the coefficient for production capacity for champagne glasses decreased from 8 to 7, and simulataneously the coefficient for storage increased from 10 to \( p \).</p>
<p>For what values of \( p \) is it worth producing champagne glasses?</p>
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\( p \leq 16\)
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\( p \leq 16.5\)
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\( p \leq 17\)
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\( p \leq 17.5\)
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