For a certain company, the cost for producing x items is 55x+300 and the revenue for selling x items is 95x−0.5x2.

Question

A) set up an expression for the profit from producing and selling x items.

B) find two value of x that will create a profit of 300$

C)is it possible for the company to make a profit of $15000

Answer 1

Profit = Revenue minus cost

P = R = C

P = 95x - .5x^2 - 55x - 300

P = -.5x^2 + 40x - 300

300 = -.5x^2 + 40x -300

.5x^2 -40x + 600 = 0

.1x^2 - 8x + 120 = 0

x^2 -80x + 1200 = 0

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

x = 20 or 60

P'(x) = -x +40 = 0

max is when the derivative = 0

x = 40

-.5(40)^2 +40(40) - 300

= 1600/2 -300 = 500 maximum which is less than 15,000