Profit: The profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and the formula is A negative quantity for P represents...

Profit: The profit P, in millions of dollars, that a manufacturer makes is a function of the number N, in millions, of items produced in a year, and the formula is

A negative quantity for P represents a negative profit—that is, a loss—and the formula is valid up to a level of 10 million items produced.

a. Express using functional notation the profit at a production level of 7 million items.

b. What is the loss at a production level of N = 0 million items?

c. Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.

d. Determine the production level that gives maximum profit, and determine the amount of the maximum profit.