Linear programming proof
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I need the proof of the Linear programming problem attached.
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Consider the LP:
Min ct x
Subject to
Ax ≥ b, x ≥ 0.
One can convert the problem to an equivalent one with equality constraints by using slack variables. Suppose that the optimal basis for the equality constrained problem is B. Prove that w = cBB-1 ≥ 0.
Where cB = coefficients of Basic variables.
B-1 = Inverse of Basis matrix.
(algebra of simplex method can be helpful in this proof)
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Solution Summary
This is a proof of a given linear program involving the basis matrix.
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Consider the LP:
Min ct x
Subject to
Ax ≥ b, x ≥ 0.
One can convert the problem to an equivalent one with equality constraints by using slack variables. Suppose that the optimal basis for the equality constrained problem is B. Prove that w = cBB-1 ≥ 0.
Where cB = coefficients of Basic variables.
B-1 = ...
Purchase this Solution
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