A division of Chapman Corporation manufactures a pager. The weekly fixed cost fo

Question

A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $29,000, 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 ; quad ; (0 leq x leq 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 2,400 units are produced and sold each week? $

Explanation / Answer

A. find the total cost function:

Total Cost + fixed cost + variable cost = $29,000 + 0.000001x3-0.01x2 +50x

B. find the total profit function

Profit = Revenue - Total Cost + R(x) - V(x)

= -29,000 + (-0.02x2+150x) - (0.000001x3-0.01x2+50x)

= - 0.000001x3 - 0.01x2 + 100x - 29,000

C. profit for the company if 2000 units are produced and sold each week

= - 0.000001(2,400)3 - 0.01(2,400)2 + 100(2,400) - 29,000

= -13824 - 57600 + 240000 - 29000

= $167,224

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