Question

The cost function for a certain company is C = 60x + 300 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 $300.

Answer 1

Answer:

The two values of x are 20 and 60

Step-by-step explanation:

Given;

cost function: C = 60x + 300

revenue function: R = 100x − 0.5x²

Profit = R - C

300 = 100x − 0.5x² - ( 60x + 300)

300 =  100x − 0.5x² - 60x - 300

300 + 300 = 100x − 0.5x² - 60x

600 = 40x - 0.5x²

600 = 40x  - ¹/₂x²

multiply both sides by 2

1200 = 80x - x²

re-write the equation

80x - x² = 1200

-x² + 80x - 1200 = 0

multiply through by (-1)

x² - 80x + 1200 = 0

factorize the quadratic equation

x² (- 60x - 20x) + 1200 = 0

x² - 60x - 20x + 1200 = 0

x(x - 60) -20(x - 60) = 0

(x - 20)(x - 60) = 0

x - 20 = 0      or x - 60 = 0

x = 20   or   60

Therefore, the two values of x are 20 and 60