Answer
(a) $-\frac{1}{10}x^2+150x$.
(b) $14,000$ dollars.
(c) $750$ units, $56,250$ dollars.
(d) $75$ dollars.
Work Step by Step
(a) Based on the given conditions, we have the revenue $R(x)=px=-\frac{1}{10}x^2+150x$.
(b) For $x=100$, we have $R(100)=-\frac{1}{10}(100)^2+150(100)=14,000$ dollars.
(c) To maximizes revenue, we need $x=-\frac{b}{2a}=-\frac{150}{2(-1/10)}=750$ units and $R(750)=-\frac{1}{10}(750)^2+150(750)=56,250$ dollars.
(d) At $x=750$, we have $p=-\frac{1}{10}(750)+150=75$ dollars.
