Write a dual problem of the following primal problem, and find optimal solution to the dual problem given that the optimal solution to the primal problem is x∗ = (0, 0, 5, 0). Maximize 2x1 + x2 + 3x3 + x4 subject to 3x1 + x2 + 2x3 + 2x4 ≤ 10 2x1 − x2 + x3 + 2x4 ≤ 15 x1 + 2x2 − 3x3 + 4x4 ≤ 12 x1, x2, x3, x4 ≥ 0

Write a dual problem of the following primal problem, and find optimal solution to the dual problem given that the optimal solution to the primal problem is x∗ = (0, 0, 5, 0). Maximize 2x1 + x2 + 3x3 + x4 subject to 3x1 + x2 + 2x3 + 2x4 ≤ 10 2x1 − x2 + x3 + 2x4 ≤ 15 x1 + 2x2 − 3x3 + 4x4 ≤ 12 x1, x2, x3, x4 ≥ 0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Write a dual problem of the following primal problem, and find optimal solution to the dual problem given that the optimal solution to the primal problem
is x∗ = (0, 0, 5, 0).
Maximize 2x1 + x2 + 3x3 + x4
subject to 3x1 + x2 + 2x3 + 2x4 ≤ 10
2x1 − x2 + x3 + 2x4 ≤ 15
x1 + 2x2 − 3x3 + 4x4 ≤ 12
x1, x2, x3, x4 ≥ 0

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