Question

The cost of producing x units of a product is C dollars, where C is given by the function C = 0.25x2 - 80x + 30000. (See the graph provided.) How many units should be produced to generate the lowest cost?

Answer 1

From calculus, to determine the maxima or minima of the graph, get the derivative of the equation and equate to zero. So, we derive first the equation of the graph and equate to zero.

C = 0.25x² - 80x + 30000
dC/dx = 0 = 0.5x - 80 + 0
0.5x = 80
x = 80/0.5
x = 160 units

The minimum cost (although not asked) is:

C = 0.25(160)² - 80(160) + 30000
C = $23,600

The answer is 160 units.