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Consider maximising 10 - x2 - 4y2 + 2xy where where x > 12. What y-value solves this maximisation problem?

Consider maximising 10 - x2 - 4y2 + 2xy where where x > 12. What y-value solves this maximisation problem?

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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Consider maximising 10 - x2 - 4y2 + 2xy where where x > 12. What y-value solves this maximisation problem? Your Answer: Answer Hide hint for Question 1 First, write the Lagrangian. Remember to rewrite the inequality constraint in the form 0 ... beforehand. You should get two first order conditions as usual from it: Ly = 0 and Ly = 0. For the third equation, using the complementary slackness condition. There are two cases: 1. constraint holds with strict equality and the multiplier is non-negative 2. constraint holds with strict inequality and the multiplier is zero Each case should come with one equation and one check to perform on the potential critical points. Find all potential critical points in every case. If there is more than one critical point, then compare them to find the maximum.
Transcribed Image Text:Consider maximising 10 - x2 - 4y2 + 2xy where where x > 12. What y-value solves this maximisation problem? Your Answer: Answer Hide hint for Question 1 First, write the Lagrangian. Remember to rewrite the inequality constraint in the form 0 ... beforehand. You should get two first order conditions as usual from it: Ly = 0 and Ly = 0. For the third equation, using the complementary slackness condition. There are two cases: 1. constraint holds with strict equality and the multiplier is non-negative 2. constraint holds with strict inequality and the multiplier is zero Each case should come with one equation and one check to perform on the potential critical points. Find all potential critical points in every case. If there is more than one critical point, then compare them to find the maximum.
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