Prove that any LP optimization problem can be transformed into the following form: minimize 0 · x subject to Ax = b, x >= 0 If the LP is feasible, then it has an optimum value of 0 If the LP is not feasible, then it has an optimal value of infinity Explain what is the dual of this LP.

Prove that any LP optimization problem can be transformed into the following form: minimize 0 · x subject to Ax = b, x >= 0 If the LP is feasible, then it has an optimum value of 0 If the LP is not feasible, then it has an optimal value of infinity Explain what is the dual of this LP.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section: Chapter Questions

Problem 17RP

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Concept explainers

Duality

Duality is a linear programming (LP) concept which states that it is possible to interpret every LP problem using two distinct methods, but they will have similar solutions. That means any LP problem can be mentioned in another equivalent form based on identical data.

Question

Prove that any LP optimization problem can be transformed into the following form:

minimize 0 · x

subject to Ax = b, x >= 0

If the LP is feasible, then it has an optimum value of 0

If the LP is not feasible, then it has an optimal value of infinity

Explain what is the dual of this LP.

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