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) (b) maximize subject to maximize subject to - 2x1 + x2 2₁-2₂ ≤ 1, 2x₁-₂ ≥ 1, 2x1 + 2x₂ ≥ 4, I1, I₂ 20 ₁ + 2x₂ -₁ + 2x₂ ≤ 6, x+3x₂ ≤ 12, I1, I2 20

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 59P
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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)
(b)
maximize
subject to
maximize
subject to
- 2x1 + x2
x₁ - x₂ ≤ 1,
2x₁₂ ≥ 1,
2x1 + 2x2 ≥ 4,
I1, I₂ 20
₁ +2.0₂
-₁ + 2x₂ ≤ 6,
1+ 3x2 ≤ 12,
I1, I2 20
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) (b) maximize subject to maximize subject to - 2x1 + x2 x₁ - x₂ ≤ 1, 2x₁₂ ≥ 1, 2x1 + 2x2 ≥ 4, I1, I₂ 20 ₁ +2.0₂ -₁ + 2x₂ ≤ 6, 1+ 3x2 ≤ 12, I1, I2 20
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