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1. Which variables are basic and which variables are nonbasic in this tableau? What basic variables are associated with rows 1, 2, and 3 of this tableau? What are the values of all the variables associated with this basic feasible solution? 2. Suppose you are maximizing the objective z. Identify which one of the following statements is correct, and answer the corresponding question. (a) The current basic feasible solution is optimal. If so, what is an optimal solution and the optimal objective value? (b) The linear program is unbounded. If so, provide a solution with objective value z = 5000 or larger. (c) At least one more iteration of the simplex algorithm is required to solve this problem. If so, identify which variable will leave the basis (go from being basic to being nonbasic), and which variable will enter the basis in the next iteration.

1. Which variables are basic and which variables are nonbasic in this tableau? What basic variables are associated with rows 1, 2, and 3 of this tableau? What are the values of all the variables associated with this basic feasible solution? 2. Suppose you are maximizing the objective z. Identify which one of the following statements is correct, and answer the corresponding question. (a) The current basic feasible solution is optimal. If so, what is an optimal solution and the optimal objective value? (b) The linear program is unbounded. If so, provide a solution with objective value z = 5000 or larger. (c) At least one more iteration of the simplex algorithm is required to solve this problem. If so, identify which variable will leave the basis (go from being basic to being nonbasic), and which variable will enter the basis in the next iteration.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 89P
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Problem 1 Consider the following simplex tableau. Row z X2 x3 x4 a5 X6 x7 x8 RHS BV 1 0 -5 4 -1 –10 0 620 z = 620 1 3 0 -2 -3 -1 1 12 2 1 1 3 1 3 6 3 1 -1 0 0 6 -4 1. Which variables are basic and which variables are nonbasic in this tableau? What basic variables are associated with rows 1, 2, and 3 of this tableau? What are the values of all the variables associated with this basic feasible solution? 2. Suppose you are maximizing the objective z. Identify which one of the following statements is correct, and answer the corresponding question. (a) The current basic feasible solution is optimal. If so, what is an optimal solution and the optimal objective value? (b) The linear program is unbounded. If so, provide a solution with objective value z = 5000 or larger. (c) At least one more iteration of the simplex algorithm is required to solve this problem. If so, identify which variable will leave the basis (go from being basic to being nonbasic), and which variable will enter the basis in the next iteration.
Transcribed Image Text:Problem 1 Consider the following simplex tableau. Row z X2 x3 x4 a5 X6 x7 x8 RHS BV 1 0 -5 4 -1 –10 0 620 z = 620 1 3 0 -2 -3 -1 1 12 2 1 1 3 1 3 6 3 1 -1 0 0 6 -4 1. Which variables are basic and which variables are nonbasic in this tableau? What basic variables are associated with rows 1, 2, and 3 of this tableau? What are the values of all the variables associated with this basic feasible solution? 2. Suppose you are maximizing the objective z. Identify which one of the following statements is correct, and answer the corresponding question. (a) The current basic feasible solution is optimal. If so, what is an optimal solution and the optimal objective value? (b) The linear program is unbounded. If so, provide a solution with objective value z = 5000 or larger. (c) At least one more iteration of the simplex algorithm is required to solve this problem. If so, identify which variable will leave the basis (go from being basic to being nonbasic), and which variable will enter the basis in the next iteration.
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