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Construct the dual of this LP and solve it using the Simplex method. 60x1 2x1 3x1 5x1 + 20x2 + 10x3 + X2 + X3 + X2 + X3 + X2 X1, X2, X3 ≥ 0 values in the final, optimal tableau for the dual, answer the questions, which all relate to the original, primal problem (above). D: ≥ 15 > 22 ≥ 30 IV

Construct the dual of this LP and solve it using the Simplex method. 60x1 2x1 3x1 5x1 + 20x2 + 10x3 + X2 + X3 + X2 + X3 + X2 X1, X2, X3 ≥ 0 values in the final, optimal tableau for the dual, answer the questions, which all relate to the original, primal problem (above). D: ≥ 15 > 22 ≥ 30 IV

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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(i) Construct the dual of this LP and solve it using the Simplex method. + 20x2 + 10x3 2x1 + X2 + X3 3x1 + X2 X3 5x1 + X2 X1, X2, X3 ≥ 0 Using the values in the final, optimal tableau for the dual, answer the following questions, which all relate to the original, primal problem (above). Minimise: 60x1 Subject to: ≥ 15 > 22 > 30 (ii) What is the optimal value of the primal LP? (iii) What are the basic variables in the optimal solution to the primal LP (iv)By how much would the optimal solution to the primal LP change if the RHS of the second constraint were to increase by 1? (v) Is the first constraint in the primal LP binding in the optimal solution (i.e. the slack variable in the first constraint is zero at optimality)? If not, how much slack is there at optimality?
Transcribed Image Text:(i) Construct the dual of this LP and solve it using the Simplex method. + 20x2 + 10x3 2x1 + X2 + X3 3x1 + X2 X3 5x1 + X2 X1, X2, X3 ≥ 0 Using the values in the final, optimal tableau for the dual, answer the following questions, which all relate to the original, primal problem (above). Minimise: 60x1 Subject to: ≥ 15 > 22 > 30 (ii) What is the optimal value of the primal LP? (iii) What are the basic variables in the optimal solution to the primal LP (iv)By how much would the optimal solution to the primal LP change if the RHS of the second constraint were to increase by 1? (v) Is the first constraint in the primal LP binding in the optimal solution (i.e. the slack variable in the first constraint is zero at optimality)? If not, how much slack is there at optimality?
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