Question

For a certain company , the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0. 5x^2.

a) set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces (hint: it is a quadratic polynomial)

b) find two values of x that will create a profit of $300

c) is it possible for the company to make a profit of $15,000​

Answer 1

Explanation:

a) Profit = Revenue - Cost = (90x - 0.5x²) - (50x + 300)

= -0.5x² + 90x - 50x - 300

= -0.5x² + 40x - 300

b) -0.5x² + 40x - 300 = 300

-0.5x² + 40x - 600 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -600):

x = 20, 60

c) -0.5x² + 40x - 300 = 15000

-0.5x² + 40x - 15300 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -15300):

x = 40±10√290i

Not possible to make a profit of $15,000