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Consider the following LPP: maximize subject to ax₁ + 1x₂ -x1+x₂ ≤2 1 2x1 + x₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). -³. (b) Solve this LPP graphically in the case when a = - (c) Use the Simplex method to solve this problem when a = -3. (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case?

Consider the following LPP: maximize subject to ax₁ + 1x₂ -x1+x₂ ≤2 1 2x1 + x₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). -³. (b) Solve this LPP graphically in the case when a = - (c) Use the Simplex method to solve this problem when a = -3. (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(1) Consider the following LPP: maximize subject to ax1 + 1x₂ -x₁ + x₂ ≤ 2 1 -X1 + X₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). (b) Solve this LPP graphically in the case when a = -³. 3 3 (c) Use the Simplex method to solve this problem when a = (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case? 4
Transcribed Image Text:(1) Consider the following LPP: maximize subject to ax1 + 1x₂ -x₁ + x₂ ≤ 2 1 -X1 + X₂ ≤ 3 X1, X20 (a) For which values of a does this LPP have an optimal solution? Hint: draw the feasible set and consider the direction of the cost vector (a, 1). (b) Solve this LPP graphically in the case when a = -³. 3 3 (c) Use the Simplex method to solve this problem when a = (d) Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case? 4
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