1. For each of the following programs: (1) Sketch the feasible region of the program and the direction of the objective function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution give the objective value for this solution. If an optimal solution does not exist, state why. (a) maximize subject to - 2x1 + x₂ x1 - x₂ ≤ 1, 2x1 - x₂ ≥ 1 2x1 + 2x₂ ≥ 4, x1, x2 > 0
1. For each of the following programs: (1) Sketch the feasible region of the program and the direction of the objective function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution give the objective value for this solution. If an optimal solution does not exist, state why. (a) maximize subject to - 2x1 + x₂ x1 - x₂ ≤ 1, 2x1 - x₂ ≥ 1 2x1 + 2x₂ ≥ 4, x1, x2 > 0
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.4: Systems Of Linear Inequalities Linear Programming
Problem 7CQ
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Transcribed Image Text:1. For each of the following programs:
(1) Sketch the feasible region of the program and the direction of the objective
function.
(2) Use you sketch to find an optimal solution to the program. State the optimal
solution give the objective value for this solution. If an optimal solution does
not exist, state why.
(a)
maximize
subject to
- 2x1 + x₂
x1 - x₂ ≤ 1,
2x1 - x₂ ≥ 1
2x1 + 2x₂ ≥ 4,
X1, X2 ≥ 0
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