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Given the following non-linear model Min x² + y² + 2x²y + 2xy + 2x²y²-8x-6y-14zy subject to 2² + y² ≤5 Choose the letter of the corresponding answers to the questions below. 1. Formulate the first two KKT Conditions A. 2x + 4xy + 2y2 + 4xy2-8-14y-2xλ = 0 2y + 2x² + 2y + 4x2y-6-14x-2yλ = 0 B. 2x + 4xy + 2y² + 4xy2-8-14y-2xλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2yλ = 0

Given the following non-linear model Min x² + y² + 2x²y + 2xy + 2x²y²-8x-6y-14zy subject to 2² + y² ≤5 Choose the letter of the corresponding answers to the questions below. 1. Formulate the first two KKT Conditions A. 2x + 4xy + 2y2 + 4xy2-8-14y-2xλ = 0 2y + 2x² + 2y + 4x2y-6-14x-2yλ = 0 B. 2x + 4xy + 2y² + 4xy2-8-14y-2xλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2yλ = 0

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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Given the following non-linear model Min x² + y² + 2x²y + 2xy + 2x²y² - 8x - 6y-14zy subject to x² + y² ≤ 5 Choose the letter of the corresponding answers to the questions below. 1. Formulate the first two KKT Conditions A. 2x + 4xy + 2y2 + 4xy2-8-14y - 2xλ = 0 2y + 2x² + 2y + 4x²y-6-14x - 2yλ = 0 B. 2x + 4xy + 2y² + 4xy2-8-14y - 2xλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2yλ = 0 C. 2x + 4xy + 2y + 4xy2-8-14y-2yλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2xλ = 0 2. Which of the following is the critical point that that minimizes the function (x, y, X)? A. (2, 1, 0) B. (0, 1, 2) C. (-1, 0, 2)
Transcribed Image Text:Given the following non-linear model Min x² + y² + 2x²y + 2xy + 2x²y² - 8x - 6y-14zy subject to x² + y² ≤ 5 Choose the letter of the corresponding answers to the questions below. 1. Formulate the first two KKT Conditions A. 2x + 4xy + 2y2 + 4xy2-8-14y - 2xλ = 0 2y + 2x² + 2y + 4x²y-6-14x - 2yλ = 0 B. 2x + 4xy + 2y² + 4xy2-8-14y - 2xλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2yλ = 0 C. 2x + 4xy + 2y + 4xy2-8-14y-2yλ = 0 2y + 2x² + 4xy + 4x²y-6-14x - 2xλ = 0 2. Which of the following is the critical point that that minimizes the function (x, y, X)? A. (2, 1, 0) B. (0, 1, 2) C. (-1, 0, 2)
3. Formulate the Hessian of the objective function (In terms of the variables x and y). A B. 4x + 4y + 8zy - 14 2+ 4y + 4y² 2+4y+4y² 4x + 4y + 8x - 14 2+ 4y + 4y² 4x + 4y + 8xy - 14 2 + 4x +4x² 4x + 4y + 8zy - 14 4x + 4y + 8x14| 2+4x+4x² 4x + 4y + 8xy - 14 2 + 4x + 4x²
Transcribed Image Text:3. Formulate the Hessian of the objective function (In terms of the variables x and y). A B. 4x + 4y + 8zy - 14 2+ 4y + 4y² 2+4y+4y² 4x + 4y + 8x - 14 2+ 4y + 4y² 4x + 4y + 8xy - 14 2 + 4x +4x² 4x + 4y + 8zy - 14 4x + 4y + 8x14| 2+4x+4x² 4x + 4y + 8xy - 14 2 + 4x + 4x²
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