Chapter 1.3, Problem 83E

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

  $\begin{array}{llll}p(x)\hfill & =\hfill & 75-3x\hfill & \text{Price–demand}\text{function}\hfill \\ R(x)\hfill & =\hfill & xp(x)=x(75-3x)\hfill & \text{Revenue}\text{function}\hfill \end{array}$

where p(x) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have domain 1 ≤ x ≤ 20.

1. (A) Sketch a graph of the revenue function in a rectangular coordinate system.
2. (B) Find the value of x that will produce the maximum revenue. What is the maximum revenue?
3. (C)         What is the wholesale price per chip that produces the maximum revenue?