Quadratic Equations

Question

For a company, the cost for producing x items is:

35x+300

The revenue of selling x items is:

75x - 0.5x²

Using the quadratic formula,find two values of x that will create a profit of $50.

Is it possible for the company to make a profit of $2500?

Answer 1

Profit P = R-C = 75x - x^2/2 - 35x -300 = -x^2/2 + 40x -300

take the derivative of the profit function and set it equal to zero for maximum profit

P' = -x + 40 = 0, x= 40

P(40) = -(40)^2/2 + 40(40) -300 = 800-300 = 500 < 2500. $2500 isn't possible

for P=50 = -x^2/2 + 40x -300

-x^2/2 +40x -250 =0

x^2 -80x + 500 = 0

x^2 -80x + 1600 = 1600-500 = 1100

(x-40)^2 = 11(100)

x-40 = 10sqr11

x = 40 + or - 10sqr11 = 73.2 or 6.8