Chapter 2.7, Problem 52E

Break-even analysis. The price–demand equation and the cost function for the production of handwoven silk scarves are given, respectively, by

  $\begin{array}{rrr}\hfill p=60-2\sqrt{x}& \hfill \text{and}& \hfill C(x)=3,000+5x\end{array}$

where x is the number of scarves that can be sold at a price of $p per unit and C(x) is the total cost (in dollars) of producing x scarves.

1. (A)   Express the revenue function in terms of x.
2. (B)   Graph the cost function and the revenue function in the same viewing window for 0 ≤ x ≤ 900. Use approximation techniques to find the break-even points correct to the nearest unit.