Chapter 4.6, Problem 21E

Maximum revenue and profit. A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are

C(x) = 72,000 + 60x

$\begin{array}{cc}p=200-\frac{x}{30}& 0\le x\le 6,000\end{array}$

1. (A) Find the maximum revenue.
2. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.
3. (C) If the government decides to tax the company $5 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?