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Find a value for the constants p and q so that ₁ = 3/2, 72 = 3/2 is the unique optimal solution of the resulting program.

Find a value for the constants p and q so that ₁ = 3/2, 72 = 3/2 is the unique optimal solution of the resulting program.

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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What is the reason for the b) answer? I cannot understand it. Please, if possible visualize why it is correct.

1. Suppose that p, q ER are both constants and consider the following linear program: maximize pr₁+qx₂ subject to ₁ + 3x2 ≤ 6, 3x1 + x2 ≤ 6, x₁ + x₂ ≥ 1, X1, X2 20 (a) Sketch the feasible region for these constraints. Solution:
Transcribed Image Text:1. Suppose that p, q ER are both constants and consider the following linear program: maximize pr₁+qx₂ subject to ₁ + 3x2 ≤ 6, 3x1 + x2 ≤ 6, x₁ + x₂ ≥ 1, X1, X2 20 (a) Sketch the feasible region for these constraints. Solution:
x2 21 (b) Find a value for the constants p and q so that x₁ = 3/2, x₂ = 3/2 is the unique optimal solution of the resulting program. Solution: By looking at the picture, one option is to set p = 1, q= 1, which gives us a direction (1, 1) that makes this the only optimal solution.
Transcribed Image Text:x2 21 (b) Find a value for the constants p and q so that x₁ = 3/2, x₂ = 3/2 is the unique optimal solution of the resulting program. Solution: By looking at the picture, one option is to set p = 1, q= 1, which gives us a direction (1, 1) that makes this the only optimal solution.
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