Find the total cost function, total profit function, and what is the profit for the company if 2200 units are produced and sold each week?

Question

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is 24000, and the variable cost for producing pagers/week in dollars is represented by the function. V(x)=0.0001x3−0.1x2+60x

The company realizes a revenue in dollars from the sale of pagers/week represented by the function.  R(x)=−0.04x2+1000x 

Find the total cost function C.

Find the total profit function P.

What is the profit for the company if 2200 units are produced and sold each week?

Answer 1

C(x) = 24000 + 0.0001 x^3 - 0.1 x^2 + 60 x

P(x) = R(x) - C(x)

= -0.04 x^2 + 1000 x - [ 24000 + 0.001 x^3 - 0.1 x^2 + 60 x ]

= -0.04x^2 + 1000x - 24000 - 0.001x^3 + 0.1 x^2 - 60x

= -0.0001x^3 + 0.06 x^2 + 940x - 24000

P(2200) = 1269600