Consider the following integer programming problem: max 5×₁ + 8x2 s.t. 2x1 + 3x2 ≤7 X1, X2 Є Z+. (i) Verify that x₁ ≤ 3 and X2 ≤ 2 are valid inequalities for the problem. (ii) Solve the problem using the branch-and-bound method. Provide the details of your choice of the next active node and the reasons for pruning nodes. You must solve the linear programming relaxations by the simplex method.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.3: Systems Of Inequalities
Problem 13E
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Consider the following integer programming problem:
max
5×₁ + 8x2
s.t.
2x1 + 3x2 ≤7
X1, X2 Є Z+.
(i) Verify that x₁ ≤ 3 and X2 ≤ 2 are valid inequalities for the problem.
(ii) Solve the problem using the branch-and-bound method. Provide the details of your
choice of the next active node and the reasons for pruning nodes.
You must solve the linear programming relaxations by the simplex method.
Transcribed Image Text:Consider the following integer programming problem: max 5×₁ + 8x2 s.t. 2x1 + 3x2 ≤7 X1, X2 Є Z+. (i) Verify that x₁ ≤ 3 and X2 ≤ 2 are valid inequalities for the problem. (ii) Solve the problem using the branch-and-bound method. Provide the details of your choice of the next active node and the reasons for pruning nodes. You must solve the linear programming relaxations by the simplex method.
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