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.

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Author:Erwin Kreyszig
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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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