Answer
When $p=40~dollars$ the maximum revenue is obtained: $R=16,000~dollars$.
Work Step by Step
We need to find the vertex of $R(p)=-10p^2+800p$
$R(p)=-10p^2+800p~~$ ($a=-10,b=800,c=0$):
$-\frac{b}{2a}=-\frac{800}{2(-10)}=40$
$f(40)=-10(40)^2+800(40)=-16000+32000=16000$
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(40,16000)$
That is, when $p=40~dollars$ the maximum revenue is obtained ($R=16,000~dollars$).
