Marginal profit: A small firm produces at most 20 widgets in a week. Its profit P , in dollars, is a function of n, the number of widgets manufactured in a week, and the formula is Recall that the...

Marginal profit: A small firm produces at most 20 widgets in a week. Its profit P , in dollars, is a function of n, the number of widgets manufactured in a week, and the formula is

Recall that the rate of change dP dn is called the marginal profit.

a. Make a graph of the profit as a function of the number of widgets manufactured in a week.

b. Determine the marginal profit if the firm produces 10 widgets in a week, and explain what your answer means in practical terms.

c. Determine the marginal profit if the firm produces 15 widgets in a week, and explain what your answer means in practical terms.

d. How many widgets should be produced in a week to maximize profit?

e. Use the calculator to determine the marginal profit at the production level you found in part