Consider the nonlinear optimization model stated below. Min 2x² 18x + 2XY+Y² - 14Y + 55 X + 4Y ≤ 8 s.t. (a) Find the minimum solution to this problem. at (x, y) = X (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 - 14Y + 55 X + 4Y ≤ 8 s.t. (a) Find the minimum solution to this problem. at (x, y) = X (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. 14Y + 55
X + 4Y ≤ 8
(a) Find the minimum solution to this problem.
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?
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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Step 1: Analysis and Introduction
VIEWStep 2: Introduce Lagrange multiplier and find all the partial derivatives
VIEWStep 3: Find the critical point and the minimum value of the function
VIEWStep 4: Examine the changes in the optimal solution when constraint is changed.
VIEWStep 5: Solve the problem for the new constraint.
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