The profit P, in thousands of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows: P = -0.2N^2 + 3.6N - 9.
(a) Express using functional notation the profit at a production level of 3 items per year. P(3) Calculate that value.
______ thousand dollars
(b) Determine the two break-even points for this manufacturer—that is, the two production levels at which the profit is zero.
N = ___ (smaller value)
N = ___ (larger value)
(c) Determine the maximum profit if the manufacturer can produce at most 16 in a year. ____ thousand dollars