(a) Suppose we are given a linear program in standard equation form maximize cx subject to Ax=b, x ≥ 0. Given two different optimal solutions y and z to this linear program, prove that every convex combination of y and z is also an optimal solution of the program. (b) Briefly explain how to use part (a) to show that every linear program has either 0, 1, or infinitely many optimal solutions.

(a) Suppose we are given a linear program in standard equation form maximize cx subject to Ax=b, x ≥ 0. Given two different optimal solutions y and z to this linear program, prove that every convex combination of y and z is also an optimal solution of the program. (b) Briefly explain how to use part (a) to show that every linear program has either 0, 1, or infinitely many optimal solutions.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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