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(Graduate students only) Consider the primal and dual problems in our standard form presented in matrix notation:

(Graduate students only) Consider the primal and dual problems in our standard form presented in matrix notation:

Advanced Engineering Mathematics
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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(Graduate students only) Consider the primal and dual problems in our standard form presented in matrix notation: Primal: Max W = y.b subject to Ay > c and Dual: Min Z = c.x subject to Ax ≤ b and x ≥ 0 y≥0 Let y* denote the optimal solution for this dual problem. Suppose that b is then replaced by b. Let X denote the optimal solution for the new primal problem. Prove that c⋅ x ≤y b
Transcribed Image Text:(Graduate students only) Consider the primal and dual problems in our standard form presented in matrix notation: Primal: Max W = y.b subject to Ay > c and Dual: Min Z = c.x subject to Ax ≤ b and x ≥ 0 y≥0 Let y* denote the optimal solution for this dual problem. Suppose that b is then replaced by b. Let X denote the optimal solution for the new primal problem. Prove that c⋅ x ≤y b
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