Average Profit: The estimate revenue and cost functions for the development of a new product are given by R(x)= -2x^2 + 8x and C(x)= 3x + 2, where x is the number of items in thousands.
a) Determine the break-even point for production.
b) The average profit function is AP(x)= P(x)/x. What production levels are required for AP(x) > 0?
-2x^2 + 8x = 3x + 2 rearrange as
2x^2 - 5x + 2 = 0
(2x - 1) ( x - 2) = 0
Two break-even pts
2x - 1 = 0 x - 2 = 0
2x = 1 x = 2 ( thousand) = 2000 items
x = 1/2 (thousand) = 500 items