A farmer wishes to fence an area next to his barn. He needs a wire fence that costs $1 per linear foot in front of the barn and and wooden fencing that costs $2 per foot on the other sides.

Find x and y so that he can enclose the maximum area if his budget for materials is $4400.

$\displaystyle A=2xy$

$\displaystyle c=(2*2x) + (1*y)=4400$

$\displaystyle 4x=4400-y$

$\displaystyle x=1100-\frac{y}{4}$

$\displaystyle A=2(1100-\frac{y}{4})y=2200y-\frac{y^2}{2}$

$\displaystyle A'=2200-y$

$\displaystyle y=2200

$

Y is supposed to be $\displaystyle \frac{2200}{3}$.

So either my area function or my constraint is wrong?