Total cost, total profit, profit with 1,400 units sold

Question

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $13,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x).
$ V(x) = 0.000001x^3 - 0.01x^2 + 50x $

 

The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x).
$ R(x) = -0.02x^2 + 150x 

(0≤x≤7500)

(a) Find the total cost function C.
C(x) =


(b) Find the total profit function P.
P(x) =


(c) What is the profit for the company if 1,400 units are produced and sold each week?
$=

Answer 1

C(x) = 0.000001x³ - 0.01x² + 50x + 13,000

 

P(x) = -0.02x² + 150x - (0.000001x³ - 0.01x² + 50x + 13,000)

 

P(x) = -0.000001x³ - 0.03x² + 100x - 13,000

 

P(14,000) = -0.000001(14,000²) - 0.03(14,000²) + 100(14,000) - 13,000 = your answer