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1. Suppose we have a linear program in standard equation form maximize cx subject to Ax = b, x ≥ 0. and suppose u, v. and w are all optimal solutions to this linear program. (a) Prove that u+v+w is a feasible solution.

1. Suppose we have a linear program in standard equation form maximize cx subject to Ax = b, x ≥ 0. and suppose u, v. and w are all optimal solutions to this linear program. (a) Prove that u+v+w is a feasible solution.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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1. Suppose we have a linear program in standard equation form maximize cTx subject to Ax = b, x ≥ 0. and suppose u, v. and w are all optimal solutions to this linear program. (a) Prove that u+v+w is a feasible solution. (b) Prove that u+v+w is an optimal solution. (c) Your proofs for (b) and (c) should work more generally for certain linear com- binations of u, v, and w. State for which linear combinations of u, v, and w your proofs still work. (You do not have to justify your answer for part (c)).
Transcribed Image Text:1. Suppose we have a linear program in standard equation form maximize cTx subject to Ax = b, x ≥ 0. and suppose u, v. and w are all optimal solutions to this linear program. (a) Prove that u+v+w is a feasible solution. (b) Prove that u+v+w is an optimal solution. (c) Your proofs for (b) and (c) should work more generally for certain linear com- binations of u, v, and w. State for which linear combinations of u, v, and w your proofs still work. (You do not have to justify your answer for part (c)).
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