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Find a value for the constants p and q so that x₁ optimal solution of the resulting program. = 0, x2 = 1 is the unique

Find a value for the constants p and q so that x₁ optimal solution of the resulting program. = 0, x2 = 1 is the unique

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 c) answer? I cannot understand it. Please, if possible visualize why it is correct.

1. Suppose that p, q € R are both constants and consider the following linear program: maximize px₁+qx₂ subject to x₁ + 3x₂ ≤ 6, 3x₁ + x₂ ≤ 6, x₁ + x₂ > 1, X1, X20 (a) Sketch the feasible region for these constraints. Solution:
Transcribed Image Text:1. Suppose that p, q € R are both constants and consider the following linear program: maximize px₁+qx₂ subject to x₁ + 3x₂ ≤ 6, 3x₁ + x₂ ≤ 6, x₁ + x₂ > 1, X1, X20 (a) Sketch the feasible region for these constraints. Solution:
x2 X1 (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. 1 is the unique 0, X₂ = (c) Find a value for the constants p and q so that x1 optimal solution of the resulting program. Solution: Again, by looking at the picture, we see that one option is to set p=−1, q = -0.5. =
Transcribed Image Text:x2 X1 (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. 1 is the unique 0, X₂ = (c) Find a value for the constants p and q so that x1 optimal solution of the resulting program. Solution: Again, by looking at the picture, we see that one option is to set p=−1, q = -0.5. =
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