Answer
When $p=6.25~dollars$ the maximum revenue is obtained ($R=468.75~dollars$).
Work Step by Step
We need to find the vertex of $R(p)=-12p^2+150p$
$R(p)=-12p^2+150p~~$ ($a=-12,b=150,c=0$)
$-\frac{b}{2a}=-\frac{-150}{2(-12)}=6.25$
$f(6.25)=-12(6.25)^2+150(6.25)=-468.75+937.50=468.75$
Vertex: $(-\frac{b}{2a},f(-\frac{b}{2a}))=(6.25,468.75)$
That is, when $p=6.25~dollars$ the maximum revenue is obtained ($R=468.75~dollars$).
