Consider the problem. 2x2 18x + 2XY+ Y2 - 16Y + 54 X + 4Y ≤ 8 (a) Find the values of X and Y that minimize the function and find the optimal solution value. Min s.t. at (x, y) = (b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by (c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate? , so the actual change is a decrease of If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is rather than what we expected in part (b).
Consider the problem. 2x2 18x + 2XY+ Y2 - 16Y + 54 X + 4Y ≤ 8 (a) Find the values of X and Y that minimize the function and find the optimal solution value. Min s.t. at (x, y) = (b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by (c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate? , so the actual change is a decrease of If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is rather than what we expected in part (b).
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:11
Consider the problem.
Min
s.t.
2x² 18x + 2XY+Y2 - 16Y + 54
X + 4Y ≤ 8
(a) Find the values of X and Y that minimize the function and find the optimal solution value.
at (X, Y) =
(b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change?
Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by
(c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate?
, so the actual change is a decrease of
If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is
rather than what we expected in part (b).
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