1. 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) maximize subject to - 4x1 + x₂ x₁ + x₂ ≤ 2, x12x2 ≤ 4, x1 + x₂ ≥7, X1, X20
1. 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) maximize subject to - 4x1 + x₂ x₁ + x₂ ≤ 2, x12x2 ≤ 4, x1 + x₂ ≥7, X1, X20
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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Transcribed Image Text:1. 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
₁ + x₂ ≤ 2,
x1 - 2x₂ ≤ 4,
x₁ + x₂ ≥ 7,
x1, x2 > 0
₁ + 2x₂
-₁ + 2x₂ ≤ 4,
1+ 3x2 ≤ 12,
x1, x₂ > 0
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