The tableaus below were obtained by performing the simplex method for a particular LP problem in which
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Question:
The tableaus below were obtained by performing the simplex method for a particular LP problem in which the objective function was being maximized. However, the tableaus have been shuffled around into a "random" order, and the value of the objective function value has been deleted.
a) for each tableau, either indicate that the solution is optimal or indicate the variable leaving the basis and the variable entering the basis with clear explanations.
b) Number the tableaus to indicate an order in which the tableaus could have occurred during the execution of the simplex method.
Tableau 1:
Basic Var | z | x1 | x2 | x3 | x4 | x5 | x6 | RHS |
z | 1 | 0 | 0 | -1125 | 0 | 1.125 | 0 | ------- |
x1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
x4 | 0 | 0 | 0 | 1.25 | 1 | 0 | 0 | 0.75 |
x2 | 0 | 0 | 1 | -1.25 | 0 | 0 | 0 | 0.25 |
x6 | 0 | 0 | 0 | 225 | 0 | -0.12 | 1 | 75 |
Tableau 2:
Basic Var | z | x1 | x2 | x3 | x4 | x5 | x6 | RHS |
z | 1 | 0 | -4500 | 4500 | 0 | 0 | 0 | ------ |
x1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
x4 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
x5 | 0 | 0 | 4000 | -5000 | 0 | 1 | 0 | 100 |
x6 | 0 | 0 | 500 | -400 | 0 | 0 | 1 | 200 |
Tableau 3:
Basic var | z | x1 | x2 | x3 | x4 | x5 | x6 | RHS |
z | 1 | 0 | 0 | 0 | 0 | 0.5 | 5 | ----- |
x1 | 0 | 1 | 0 | 0 | 0 | 0.001 | 0 | 0.667 |
x4 | 0 | 0 | 0 | 0 | 1 | 0 | -0.01 | 0.333 |
x2 | 0 | 0 | 1 | 0 | 0 | 0 | 0.006 | 0.667 |
x3 | 0 | 0 | 0 | 1 | 0 | 0 | 0.004 | 0.333 |
Tableau 4:
Basic Var | z | x1 | x2 | x3 | x4 | x5 | x6 | RHS |
z | 1 | -4500 | -4100 | 0 | 0 | 0 | 0 | ----- |
x3 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
x4 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
x2 | 0 | 5000 | 4000 | 0 | 0 | 1 | 0 | 6000 |
x6 | 0 | 400 | 500 | 0 | 0 | 0 | 1 | 600 |
Related Book For
Smith and Roberson Business Law
ISBN: 978-0538473637
15th Edition
Authors: Richard A. Mann, Barry S. Roberts
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