Chapter 2.7, Problem 50E

Revenue, cost, and profit. The total cost and the total revenue (in dollars) for the production and sale of x hair dryers are given, respectively, by

  $\begin{array}{rrr}\hfill C(x)=5x+2,340& \hfill \text{and}& \hfill R(x)=40x-0.1x^2\\ \hfill & \hfill & \hfill 0\le x\le 400\end{array}$

1. (A)   Find the value of x where the graph of R(x) has a horizontal tangent line.
2. (B)   Find the profit function P(x).
3. (C)   Find the value of x where the graph of P(x) has a horizontal tangent line.
4. (D)   Graph C(x), R(x), and P(x) on the same coordinate system for 0 ≤ x ≤ 400. Find the break-even points. Find the x intercepts of the graph of P(x).