Answer
$x=25~ft$
$y=\frac{100}{3}~ft$
$A=5000~ft^2$
Work Step by Step
We need to find the vertex of $A=-\frac{8}{3}x^2+\frac{400}{3}x$
$A=-\frac{8}{3}x^2+\frac{400}{3}x~~$ ($a=-\frac{8}{3},b=\frac{400}{3}x,c=0$):
$-\frac{b}{2a}=-\frac{\frac{400}{3}}{2(-\frac{8}{3})}=-\frac{400}{3}(-\frac{3}{16})=25$
$f(25)=-\frac{8}{3}(25)^2+\frac{400}{3}(25)=\frac{5000}{3}$
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(25,\frac{5000}{3})$
That is, when $x=25~ft$, $A=\frac{5000}{3}~ft^2$
$y=\frac{200-4x}{3}~~$ (item(a))
$y=\frac{200-4(25)}{3}=\frac{100}{3}~ft$
