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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)

F

_{x}= 1 - 2y - 2λ(x-1)

F

_{y}= -2 + 2x - 2λ(y+1/2)

F

_{λ}= -((x -1)

^{2}+(y + 1/2)

^{2}-2))