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<!doctype html>
<html lang="en">
<head>
<title>Assignment 1 Combinatorial Optimization</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
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<a class="nav-link" href="instructionsAssignment1.html">Instructions</a>
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<li class="nav-item">
<a class="nav-link" href="question1.html">Exercise 1</a>
</li>
<li class="nav-item">
<a class="nav-link" href="question2.html">Exercise 2</a>
</li>
<li class="nav-item active">
<a class="nav-link" href="#">Exercise 3</a>
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<li class="nav-item">
<a class="nav-link" href="question4.html">Exercise 4</a>
</li>
</ul>
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<div class="jumbotron text-center">
<h1>Combinatorial Optimization 2020-2021</h1>
<h2>Exercise 3</h2>
</div>
</div>
<form id="my_form">
<div class="container">
<hr>
<h4>MIP with first formulation</h4>
<hr>
<h6>Question 1</h6>
<p>
<label for="_num_auto_decimals_2_question_1_ip_val_1_id">For the first formulation,
state the optimal MIP objective value.</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_1_ip_val_1_id" value="0"
name="_num_auto_decimals_2_question_1_ip_val_1"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
<br>
<h6>Question 2</h6>
<p>
<label for="_numarea_manual_decimals_2_question_2_ip_sol_x_1_id__shadow">For the
first formulation, state the x-matrix of the optimal MIP solution. Your answer
should be a numeric 100 x 100 matrix.</label>
</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_1_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_2_ip_sol_x_1_id__shadow','_numarea_manual_decimals_2_question_2_ip_sol_x_1_id_','_numarea_manual_decimals_2_question_2_ip_sol_x_1_id__label',100,100,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_1_id_"
name="_numarea_manual_decimals_2_question_2_ip_sol_x_1"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_2_ip_sol_x_1_id_"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_1_id__label"></label>
<br>
<h6>Question 3</h6>
<p>
<label for="_numarea_manual_decimals_2_question_3_ip_sol_y_1_id__shadow">For the
first formulation, state the y-vector of the optimal MIP solution as a
column vector. Your answer should be a numeric 100 x 1 matrix.</label>.
</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_1_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_3_ip_sol_y_1_id__shadow','_numarea_manual_decimals_2_question_3_ip_sol_y_1_id_','_numarea_manual_decimals_2_question_3_ip_sol_y_1_id__label',100,1,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_1_id_"
name="_numarea_manual_decimals_2_question_3_ip_sol_y_1"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_3_ip_sol_y_1_id_"
id="_numarea_manual_decimals_2_question_3_ip_sol_y_1_id__label"></label>
<br>
<h6>Question 4</h6>
<p>
<label for="_num_auto_decimals_2_question_4_ip_time_1_id">For the first formulation,
state the running time needed to solve the MIP to optimality.
Round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_4_ip_time_1_id" value="0"
name="_num_auto_decimals_2_question_4_ip_time_1"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
<br>
<h6>Question 5</h6>
<p>
<label for="nodes_ip_1">For the first formulation, state the number of nodes needed
to solve the MIP to optimality.</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="nodes_ip_1" value="0"
name="_num_auto_decimals_0_question_5_ip_nodes_1"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
</div>
<div class="container">
<hr>
<h4>LP with first formulation</h4>
<hr>
<h6>Question 6</h6>
<p>
<label for="value_lp_1">For the first formulation, state the optimal LP relaxation
objective value.
If needed, round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control" id="value_lp_1" step="0.01"
name="_num_auto_decimals_2_question_6_lp_val_1" value="0" required>
</div>
<br>
<h6>Question 7</h6>
<p>
<label for="time_lp_1">For the first formulation, state the running time needed to
solve the LP relaxation to optimality.
Round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control" id="time_lp_1"
name="_num_auto_decimals_2_question_7_lp_time_1" step="0.01" value="0" required>
</div>
<br>
</div>
<div class="container">
<hr>
<h4>MIP with second formulation</h4>
<hr>
<h6>Question 8</h6>
<p>
<label for="value_ip_2">For the second formulation,
state the optimal MIP objective value.</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="value_ip_2"
value="0"
min="-Infinity" max="Infinity" step="0.01" name="_num_auto_decimals_2_question_8_ip_val_2"
required>
</div>
<br>
<h6>Question 9</h6>
<p>
<label for="_numarea_manual_decimals_2_question_2_ip_sol_x_2_id__shadow">For the
second formulation, state the x-matrix of the optimal MIP solution. Your answer
should be a numeric 100 x 100 matrix.</label>
</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_2_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_2_ip_sol_x_2_id__shadow','_numarea_manual_decimals_2_question_2_ip_sol_x_2_id_','_numarea_manual_decimals_2_question_2_ip_sol_x_2_id__label',100,100,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_2_id_"
name="_numarea_manual_decimals_2_question_9_ip_sol_x_2"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_2_ip_sol_x_2_id_"
id="_numarea_manual_decimals_2_question_2_ip_sol_x_2_id__label"></label>
<br>
<h6>Question 10</h6>
<p>
<label for="_numarea_manual_decimals_2_question_10_ip_sol_y_2_id__shadow">For the
second formulation, state the y-vector of the optimal MIP solution as a column
vector. Your answer should be a numeric 100 x 1 matrix.</label>
</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_2_id__shadow"
required
oninput="updateTextAreaAndLabel('_numarea_manual_decimals_2_question_10_ip_sol_y_2_id__shadow','_numarea_manual_decimals_2_question_10_ip_sol_y_2_id_','_numarea_manual_decimals_2_question_10_ip_sol_y_2_id__label',100,1,2)"></textarea>
<p>The parsed result is:</p>
<textarea class="form-control" rows="5"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_2_id_"
name="_numarea_manual_decimals_2_question_10_ip_sol_y_2"
readonly="true"></textarea>
<label for="_numarea_manual_decimals_2_question_10_ip_sol_y_2_id_"
id="_numarea_manual_decimals_2_question_10_ip_sol_y_2_id__label"></label>
<br>
<h6>Question 11</h6>
<p>
<label for="_num_auto_decimals_2_question_4_ip_time_2_id">For the second
formulation, state the running time needed to solve the MIP to optimality.
Round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_auto_decimals_2_question_4_ip_time_2_id" value="0"
name="_num_manual_decimals_2_question_11_ip_time_2"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
<br>
<h6>Question 12</h6>
<p>
<label for="_num_manual_decimals_0_question_12_ip_nodes_2_id">For the seond formulation, state the
number of nodes needed
to solve the MIP to optimality.</label>
</p>
<div class="input-group">
<input type="number" class="form-control"
id="_num_manual_decimals_0_question_12_ip_nodes_2_id"
name="_num_manual_decimals_0_question_12_ip_nodes_2" value="0"
min="-Infinity" max="Infinity" step="0.01" required>
</div>
<br>
</div>
<div class="container">
<hr>
<h4>LP with second formulation</h4>
<hr>
<h6>Question 13</h6>
<p>
<label for="_num_auto_decimals_2_question_13_lp_val_2_id">For the second formulation, state the optimal
LP relaxation
objective value.
If needed, round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control" id="_num_auto_decimals_2_question_13_lp_val_2_id"
name="_num_auto_decimals_2_question_13_lp_val_2" step="0.01" value="0" required>
</div>
<br>
<h6>Question 14</h6>
<p>
<label for="time_lp_2">For the second formulation, state the running time needed to
solve the LP relaxation to optimality.
Round your answer to 2 decimal places.
</label>
</p>
<div class="input-group">
<input type="number" class="form-control" id="time_lp_2"
name="_num_manual_decimals_2_question_14_lp_time_2" step="0.01" value="0" required>
</div>
<br>
</div>
<div class="container">
<hr>
<h4>Theory</h4>
<hr>
<h6>Question 15</h6>
<p>In general for this problem, the feasible region of the MIP for the second
formulation is:</p>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_1"
name="_mc_auto_question_15_mip_feas"
value="Equal to that for the first formulation.">
<label for="_mc_auto_question_11_time_id___ans_1">Equal to that for the first
formulation.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_2"
name="_mc_auto_question_15_mip_feas"
value=" subset of that for the first formulation.">
<label for="_mc_auto_question_11_time_id___ans_2">A subset of that for the first
formulation.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_11_time_id___ans_3"
name="_mc_auto_question_15_mip_feas"
value=">A superset of that for the first formulation.">
<label for="_mc_auto_question_11_time_id___ans_3">A superset of that for the first
formulation.</label>
</div>
<div class="radio">
<input
type="radio"
id="_mc_auto_question_11_time_id___ans_4"
name="_mc_auto_question_15_mip_feas"
value="Neither a subset nor a superset of that for the first formulation"
checked>
<label for="_mc_auto_question_11_time_id___ans_4">Neither a subset nor a superset of
that for the first formulation.</label>
</div>
<div class="radio">
<input type="radio" value="None of the above."
id="_mc_auto_question_11_time_id___ans_5" name="_mc_auto_question_15_mip_feas">
<label for="_mc_auto_question_11_time_id___ans_5">None of the above</label>
</div>
<br>
<h6>Question 16</h6>
<p>In general for this problem, the feasible region of the LP relaxation for the second
formulation is:</p>
<div class="radio">
<input type="radio"
id="_mc_auto_question_16_time_id___ans_1"
name="_mc_auto_question_16_lp_feas"
value="Equal to that for the first formulation.">
<label for="_mc_auto_question_16_time_id___ans_1">Equal to that for the first
formulation.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_16_time_id___ans_2"
name="_mc_auto_question_16_lp_feas"
value="A subset of that for the first formulation.">
<label for="_mc_auto_question_16_time_id___ans_2">A subset of that for the first
formulation.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_16_time_id___ans_3"
name="_mc_auto_question_16_lp_feas"
value="A superset of that for the first formulation.">
<label for="_mc_auto_question_16_time_id___ans_3">A superset of that for the first
formulation.</label>
</div>
<div class="radio">
<input
type="radio"
id="_mc_auto_question_16_time_id___ans_4"
name="_mc_auto_question_16_lp_feas"
value="Neither a subset nor a superset of that for the first formulation."
checked>
<label for="_mc_auto_question_16_time_id___ans_4">Neither a subset nor a superset of
that for the first formulation.</label>
</div>
<div class="radio">
<input type="radio" value="None of the above."
id="_mc_auto_question_16_time_id___ans_5" name="_mc_auto_question_16_lp_feas">
<label for="_mc_auto_question_16_time_id___ans_5">None of the above.</label>
</div>
<br>
<h6>Question 17</h6>
<p>In general for this problem, when applying the branch-and-bound algorithm:</p>
<div class="radio">
<input type="radio"
id="_mc_auto_question_17_time_id___ans_1"
name="_mc_auto_question_17_bnb"
value="The first formulation is preferred.">
<label for="_mc_auto_question_17_time_id___ans_1">The first formulation is
preferred.</label>
</div>
<div class="radio">
<input type="radio"
id="_mc_auto_question_17_time_id___ans_2"
name="_mc_auto_question_17_bnb"
value="The second formulation is preferred.">
<label for="_mc_auto_question_17_time_id___ans_2">The second formulation is
preferred.</label>
</div>
<div class="radio">
<input type="radio" value="None of the above."
id="_mc_auto_question_17_time_id___ans_3"
name="_mc_auto_question_17_bnb">
<label for="_mc_auto_question_17_time_id___ans_3">None of the above.</label>
</div>
</div>
</form>
<div class="container">
<button type="submit" class="btn btn-primary btn-lg btn-block handin-btn"
onclick="download_file('Exercise3')">
Download Form
</button>
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