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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).

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter12: Algebra Of Matrices
Section12.CR: Review Problem Set
Problem 37CR
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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).
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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