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Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39 x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. 2*x1 + x2 + x3 + x4 <= 2 x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. x2 + x3 + x4 <= 2 x1 + x2 <= 1 x1 + x3 <= 1 x1 + x4 <= 1 x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1

Compare the LP relaxations of the three integer optimization problems: (Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39 x1, x2, x3, x4 \in {0,1} (Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. 2*x1 + x2 + x3 + x4 <= 2 x1, x2, x3, x4 \in {0,1} (Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4 s.t. x2 + x3 + x4 <= 2 x1 + x2 <= 1 x1 + x3 <= 1 x1 + x4 <= 1 x1, x2, x3, x4 \in {0,1} Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization? Problem 2 Problem 3 Problem 1

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter8: Evolutionary Solver: An Alternative Optimization Procedure
Section: Chapter Questions
Problem 20P
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1. Compare the LP relaxations of the three integer optimization problems:

(Problem 1) max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t. 28*x1 + 15*x2 + 13*x3 + 12*x4 <= 39
x1, x2, x3, x4 \in {0,1}

(Problem 2) max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t. 2*x1 + x2 + x3 + x4 <= 2
x1, x2, x3, x4 \in {0,1}

(Problem 3) max 14*x1 + 8*x2 + 6*x3 + 6*x4
s.t. x2 + x3 + x4 <= 2
x1 + x2 <= 1
x1 + x3 <= 1
x1 + x4 <= 1
x1, x2, x3, x4 \in {0,1}

Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization?

  1. Problem 2
  2. Problem 3
  3. Problem 1
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