5. Consider the following problem = 2x₁ - x₂ + x3, Maximize Z = 3x₁ + x₂ + x3 ≤ 6 (resource 1) x₁ - x₂ + 2x3 ≤ 1 (resource 2) X₁ + X₂ X3 ≤ 2 (resource 3) and x₁ ≥ 0, X₂ ≥ 0, x3 ≥ 0. The final tableau of the simplex method is subject to Bas Eq Var No Z Z 0 1 X4 1 0 X1 2 0 X2 3 0 X1 0 0 1 0 X₂ 0 0 0 1 Coefficient of X3 X4 1.5 1 0.5 -1.5 0 1 0 0 X5 1.5 -1 0.5 -0.5 X6 0.5 -2 0.5 0.5 Right Side 2.5 1 1.5 0.5 (a) What is the shadow price for each resource? (b) If we can increase all resource capacity, which resource has the priority? (c) If Z is the profit measured in million, and the cost to increase each resource by one unit is $1 million, should we increase the resource 1 by one unit? What about resource 2 and resource 3?

5. Consider the following problem = 2x₁ - x₂ + x3, Maximize Z = 3x₁ + x₂ + x3 ≤ 6 (resource 1) x₁ - x₂ + 2x3 ≤ 1 (resource 2) X₁ + X₂ X3 ≤ 2 (resource 3) and x₁ ≥ 0, X₂ ≥ 0, x3 ≥ 0. The final tableau of the simplex method is subject to Bas Eq Var No Z Z 0 1 X4 1 0 X1 2 0 X2 3 0 X1 0 0 1 0 X₂ 0 0 0 1 Coefficient of X3 X4 1.5 1 0.5 -1.5 0 1 0 0 X5 1.5 -1 0.5 -0.5 X6 0.5 -2 0.5 0.5 Right Side 2.5 1 1.5 0.5 (a) What is the shadow price for each resource? (b) If we can increase all resource capacity, which resource has the priority? (c) If Z is the profit measured in million, and the cost to increase each resource by one unit is $1 million, should we increase the resource 1 by one unit? What about resource 2 and resource 3?

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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