Answer
A) $27$ million tennis rockets.
B) $R(p)=0.09p^3-4.2p^2+51p$
C) About $18.2$ billion
Work Step by Step
Given $$\begin{aligned}
S(p) &= 0.09p^2-4.2p+51.
\end{aligned}$$ Part A
When the price $p= \$40$, the number of car tennis rocket supplied by the manufacturer is: $$\begin{aligned}
S(p) &= 0.09\cdot 40^2-4.2\cdot 40+51\\
&= 27\ \text{million}.
\end{aligned}$$ Part B
The revenue function is the product of the supply function, $S$ and the price, $p$. It is given by $$\begin{aligned}
R(p) &= pS(p) \\
&= p(0.09p^2-4.2p+51)\\
&=0.09p^3-4.2p^2+51p.
\end{aligned}$$ Part C
Set $p= 75$ to estimate the revenue.
$$\begin{aligned}
R(90)&= 0.09\cdot 75^3-4.2\cdot 75^2+51\cdot 75\\
&=\$18168.75\ \text{million}.
\end{aligned}$$
