For each of the following linear programs: (1) Sketch the feasible region of the linear program and the direction of the objec- tive function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. If an optimal solution does not exist, state why. (a) (b) - 4x₁ + x₂ subject to x₁ + x₂ ≤ 2, x1 - 2x₂ ≤ 4, x₁ + x₂ ≥ 7, X1, X₂0 maximize maximize subject to ₁ + 2x₂ 1x1 -₁ + 2x₂ ≤ 4, 1+ 3x2 ≤ 12, X1, X20

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 13T
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Question
For each of the following linear programs:
(1) Sketch the feasible region of the linear program and the direction of the objec-
tive function.
(2) Use you sketch to find an optimal solution to the program. State the optimal
solution and give the objective value for this solution. If an optimal solution
does not exist, state why.
(a)
(b)
maximize
subject to
maximize
subject to
- 4x1 + x₂
x₁ + x₂ ≤ 2,
x1 - 2x₂ ≤ 4,
x₁ + x₂ ≥ 7,
X1, X20
₁ + 2x₂
x₁ + 2x₂ ≤ 4,
x1 + 3x2 ≤ 12,
X1, X2 20
Transcribed Image Text:For each of the following linear programs: (1) Sketch the feasible region of the linear program and the direction of the objec- tive function. (2) Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. If an optimal solution does not exist, state why. (a) (b) maximize subject to maximize subject to - 4x1 + x₂ x₁ + x₂ ≤ 2, x1 - 2x₂ ≤ 4, x₁ + x₂ ≥ 7, X1, X20 ₁ + 2x₂ x₁ + 2x₂ ≤ 4, x1 + 3x2 ≤ 12, X1, X2 20
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