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 as follows.
p = 10n ? n2 ? 4.49
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 6 million items per year.
p( )
calculate the value. (round your answer to two decimal places.)
million dollars
(b) what is the loss at a production level of n = 0 million items? (round your answer to two decimal places.)
million dollars
(c) determine the two break-even points for this manufacturer — that is, the two production levels at which the profit is zero. (round your answers to two decimal places.)
million items (smaller value)
million items (larger value)
(d) determine the production level that gives maximum profit, and determine the amount of the maximum profit. (round your answers to two decimal places.)