A Norman window is constucted by adjoining a semi-circle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet.

I know the equations:

$\displaystyle A=xy+\frac {pi*x^2}{4}$

$\displaystyle P=x+2y+\frac {pi*x}{2}=16$

(Don't know how to make the pi symbol in LaTeX,

)

I tried to solve it multiple times but each time I end with something not possible, such as 4+1=0(just an example). Any help is appreciated, thanks. Here is a drawing of the figure, sorry for my bad paint skills.