The cost function for a certain company

Question

The cost function for a certain company is C = 40x + 800

 and the revenue is given by R = 100x − 0.5x².

 Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $800.

Answer 1

100x - 0.5x² - (40x + 800) = 800

100x - 0.5x² - 40x - 800 = 800

0.5x² - 60x + 1600 = 0

We need two factors of 0.5(1600) = 800 that have a sum of -60.

0.5x² - 40x - 20x + 1600 = 0

0.5x(x - 80) - 20(x - 80) = 0

(0.5x - 20)(x - 80) = 0

In order for the left side to equal 0, one of the factors has to equal 0.

0.5x - 20 = 0

0.5x = 20

x = 40

x - 80 = 0

x = 80