Chapter 4.2, Problem 43E

In Exercises 27–44, calculate total cost (disregarding any fixed costs) or total profit.

43. Total cost from marginal cost. Henson Hatmakers finds that the marginal cost of manufacturing $x$ baseball caps is given by

$C\text{'}\left(x\right)=\left\{\begin{array}{l}6.50,0\le x\le 20\\ 5.50,20<x\le 35\\ 3.75,x>35,\end{array}\right.$

where $C\text{'}\left(x\right)$ is in dollars per cap. The price breaks are not retroactive; that is, if 25 caps are manufactured, the first 20 are produced at $6.50 per cap, and the next 5 at $5.50 per cap. Find the total cost of manufacturing 60 caps.