Answer
When $p=24~dollars$ the maximum revenue is obtained ($R=14,400~dollars$).
Work Step by Step
We need to find the vertex of $R(p)=-25p^2+1200p$
$R(p)=-25p^2+1200p~~$ ($a=-25,b=1200,c=0$)
$-\frac{b}{2a}=-\frac{-1200}{2(-25)}=24$
$f(24)=-25(24)^2+1200(24)=-14400+28800=14400$
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(24,14400)$
That is, when $p=24~dollars$ the maximum revenue is obtained ($R=14,400~dollars$).
