Chapter 1.3, Problem 78E

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

  $\begin{array}{llll}p(x)\hfill & =\hfill & 2,000-6x\hfill & \text{Price–demand}\text{function}\hfill \\ R(x)\hfill & =\hfill & xp(x)\hfill & \text{Revenue}\text{function}\hfill \\ \hfill & =\hfill & x(2,000-60x)\hfill & \hfill \end{array}$

where p(x) is the wholesale price in dollars at which x thousand computers can be sold, and R(x) is in thousands of dollars. Both functions have domain 1 ≤ x ≤ 25.

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 to the nearest thousand dollar’s?
3. (C)         What is the wholesale price per computer (to the nearest dollar) that produces the maximum revenue?