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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

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

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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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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