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Solution: Form the Lagrangian: Next, solve the system , or max f(x, y) = -xy +3 Subject to: x² + xy + y² = 3 Verify if max or min L(x, y, A) = (-xy + 3) + A (x² + xy + y² − 3) A (2r+y)-y=0 (x+2y)-x=0 [x² + xy + y²-3=0 The system has the following real solutions: (x, y, A) = (-1,-1, 1/3), (x, y, A) = (1, 1, 1/3) (x, y, A) = (-√3, √3, -1), (x, y, A) = (√3, -√3, -1)

Solution: Form the Lagrangian: Next, solve the system , or max f(x, y) = -xy +3 Subject to: x² + xy + y² = 3 Verify if max or min L(x, y, A) = (-xy + 3) + A (x² + xy + y² − 3) A (2r+y)-y=0 (x+2y)-x=0 [x² + xy + y²-3=0 The system has the following real solutions: (x, y, A) = (-1,-1, 1/3), (x, y, A) = (1, 1, 1/3) (x, y, A) = (-√3, √3, -1), (x, y, A) = (√3, -√3, -1)

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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how to solve the systems of equations please teach  explain step by step also  Verify if max or min

Solution: Form the Lagrangian: Next, solve the system , or maxf(x, y) = -xy+3 Subject to: x² + xy + y² = 3 Verify if max or min L(x, y, A) = (-xy + 3) + λ (x² + xy + y² − 3) ak 0 0 X (2x+y)- y = 0 X(x+2y)-x=0 x² + xy + y²-3=0 The system has the following real solutions: (x, y, λ) = (-1,-1,1/3), (x, y, X) = (1, 1, 1/3) (x, y, X) = (-√3, √3,-1), (x, y, X) = (√3,-√3,-1)
Transcribed Image Text:Solution: Form the Lagrangian: Next, solve the system , or maxf(x, y) = -xy+3 Subject to: x² + xy + y² = 3 Verify if max or min L(x, y, A) = (-xy + 3) + λ (x² + xy + y² − 3) ak 0 0 X (2x+y)- y = 0 X(x+2y)-x=0 x² + xy + y²-3=0 The system has the following real solutions: (x, y, λ) = (-1,-1,1/3), (x, y, X) = (1, 1, 1/3) (x, y, X) = (-√3, √3,-1), (x, y, X) = (√3,-√3,-1)
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