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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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Chapter : sensitivity analysis in linear programming

Problem 1 The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax = b, x ≥ 0 1 Cj By X3 1 1 -4 Св 2 3 X₁ X₂ 2 X1 1 0 3 X2 0 1 0 0 X4 3 -1 -3 0 X5 -1 2 -4 RHS Ratio 1 2 Z=8 C Row 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?
Transcribed Image Text:Problem 1 The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax = b, x ≥ 0 1 Cj By X3 1 1 -4 Св 2 3 X₁ X₂ 2 X1 1 0 3 X2 0 1 0 0 X4 3 -1 -3 0 X5 -1 2 -4 RHS Ratio 1 2 Z=8 C Row 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?
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