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}
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}
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 35CR: Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.
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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?
A) Problem 2
B) Problem 1
C) Problem 3
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