A company finds that it can make a profit of P dollars each month by selling x patterns, according to the formula P ( x ) = − .002 x 2 + 4.5 x − 800 .

Question

How many patterns must it sell each month to have a maximum profit?

To attain maximum profit they must sell ___ patterns.

What is the maximum profit?

The max profit is $___.

Answer 1

P(x) = .002x^2 + 4.5x -800

P'(x) = .004x + 4.5 = 0

x= 4.5/.004 = 1125 = profit maximizing output

P(1125) = .002(1125)^2 + 4.5(1125) - 800 = 2531.25 + 5062.5 -800 = 7593.75 -800 = $6,993.75 = max profit