Consider the nonlinear optimization model stated below. Min 2x² 18x + 2XY+Y2-12Y + 53 s.t. X + 4Y ≤ 8 (a) Find the minimum solution to this problem. 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? If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is , so the actual change is a decrease of rather than what we expected in part (b).
Consider the nonlinear optimization model stated below. Min 2x² 18x + 2XY+Y2-12Y + 53 s.t. X + 4Y ≤ 8 (a) Find the minimum solution to this problem. 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? If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is , so the actual change is a decrease of 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:Consider the nonlinear optimization model stated below.
2x² 18x + 2XY+Y² - 12Y + 53
X + 4Y ≤ 8
Min
s.t.
(a) Find the minimum solution to this problem.
at (x, y) =
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?
If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is
so the actual change is a decrease of
rather than what we expected in part (b).
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