Chapter 4.4, Problem 81E

Marginal Profit Paramount Electronics has an annual profit given by

$P=-100,000+5,000q-0.25q^2\text{ dollers,}$ where q is the number of laptop computers it sells each year. The number of laptop computers it can make and sell each year depends on the number n of electrical engineers Paramount employs, according to the equation

$q=30n+0.01n^2.$

Use the chain rule to find ${\frac{dP}{dn}|}_{n=10}$ andinterpret the result. [HINT: See Example 4.]