Lagrange Multiplier Question

  • Thread starter tasveerk
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  • #1
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Homework Statement


Find the product of the maximal and the minimal values of the function
z = x - 2y + 2xy
in the region
(x -1)2+(y + 1/2)2≤2

Homework Equations





The Attempt at a Solution


I have taken the partial derivatives and set-up the problem, but I am having difficulty solving for x and y.
F(x,y) = x-2y+2xy-λ((x -1)2+(y + 1/2)2 -2)
Fx = 1 - 2y - 2λ(x-1)
Fy = -2 + 2x - 2λ(y+1/2)
Fλ = -((x -1)2+(y + 1/2)2 -2))
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


Find the product of the maximal and the minimal values of the function
z = x - 2y + 2xy
in the region
(x -1)2+(y + 1/2)2≤2

Homework Equations





The Attempt at a Solution


I have taken the partial derivatives and set-up the problem, but I am having difficulty solving for x and y.
F(x,y) = x-2y+2xy-λ((x -1)2+(y + 1/2)2 -2)
Fx = 1 - 2y - 2λ(x-1)
Fy = -2 + 2x - 2λ(y+1/2)
Fλ = -((x -1)2+(y + 1/2)2 -2))

The first two equations are linear in x and y, so you can solve for x and y as functions of λ.

RGV
 

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