Chapter 2.3, Problem 69E

Revenue. The marketing research department for a company that manufactures and sells memory chips for microcomputers established the following price-demand and revenue functions.

$\begin{array}{l}p\left(x\right)=75-3x\text{ Price}-\text{demand}\text{function}\\ R\left(x\right)=xp\left(x\right)=x\left(75-3x\right)Revenuefunction\end{array}$

Where $p\left(x\right)$ is the wholesale price in dollars at which $x$ million chips can be sold, and $R\left(x\right)$

is in millions of dollars. Both functions have domain $1\le x\le 20$

(A) Sketch a graph of the revenue function in a rectangular coordinate system.

(B) Find the value of $x$ that will produce the maximum revenue. What is the maximum revenue?

(C) What is the wholesale price per chip that produces the maximum revenue?