Chapter 4, Problem 58RE

Maximum revenue and profit. A company manufactures and sells x e-book readers per month. The monthly cost and price-demand equations are, respectively,

     $\begin{array}{l}C\left(x\right)=350x+50,000\\ \begin{array}{cc}p=500-0.025x& 0\le x\le 20,000\end{array}\end{array}$

(A) Find the maximum revenue.

(B) How many readers should the company manufacture each month to maximize its profit? What is the maximum monthly profit? How much should the company charge for each reader?

(C) If the government decides to tax the company $20 for each reader it produces, how many readers should the company manufacture each month to maximize its profit? What is the maximum monthly profit? How much should the company charge for each reader?