Problem I The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax = b, x ≥ 0 Cj Bv X₁ X₂ Св 2 3 C Row 2 X1 1 0 0 3 X2 0 1 X3 1 1 -4 0 X4 3 -1 -3 0 X5 -1 2 -4 RHS Ratio 1 2 Z=8 Assume that (x4, X5) were the initial basic variables. (a) How much can c3 be increased before the current basis is no longer optimal? Find an optimal solution when c3 = = 6. (b) How much can c₁ be varied so that the given basis (x₁, x2) is still optimal? (c) How much can b₂ (the original value) be varied before the given basis (x1, x2) is no longer feasible?

Problem I The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax = b, x ≥ 0 Cj Bv X₁ X₂ Св 2 3 C Row 2 X1 1 0 0 3 X2 0 1 X3 1 1 -4 0 X4 3 -1 -3 0 X5 -1 2 -4 RHS Ratio 1 2 Z=8 Assume that (x4, X5) were the initial basic variables. (a) How much can c3 be increased before the current basis is no longer optimal? Find an optimal solution when c3 = = 6. (b) How much can c₁ be varied so that the given basis (x₁, x2) is still optimal? (c) How much can b₂ (the original value) be varied before the given basis (x1, x2) is no longer feasible?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.3: Capital Budgeting Models

Problem 3P: Solve Problem 1 with the extra assumption that the investments can be grouped naturally as follows:...

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