Answer
A) $60$
B) $R(p)= 0.009p^3-0.5p^2+20p$
C) $\$4,311,000$
Work Step by Step
Part A
Given $$\begin{aligned}
S(p) &= 0.009p^2-0.5p+20.
\end{aligned}$$ When the price $p= \$100$, the number of car stereos supplied by the manufacturer is: $$\begin{aligned}
S(p) &= 0.009\cdot 100^2-0.5\cdot 100+20\\
&= 60\ \text{thousand}.
\end{aligned}$$ Part B
The revenue function is the product of the supply function, $S$ and the price, $p$. It is given by
$$\begin{aligned}
R(p) &= pS(p) \\
&= p(0.009p^2-0.5p+20)\\
&=0.009p^3-0.5p^2+20p.
\end{aligned}$$ Part C
Set $p= 90$ to estimate the revenue.
$$\begin{aligned}
R(90)&= 0.009\cdot 90^3-0.5\cdot 90^2+20\cdot 90\\
&=\$4,311,000.
\end{aligned}$$
