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 $23,000, 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 1,900 units are produced and sold each week? $

Explanation / Answer

a) Total Cost = Fixed cost + Variable Cost

=> 15000 + 0.000001x^3 - 0.01x^2 + 50x

=> 0.000001x^3 - 0.01x^2 + 50x + 15000

b) Profit = Revenue - Cost

P(x) = x * R(x) - Total Cost

=> x * (-0.02x + 150x) - (0.000001x^3 - 0.01x^2 + 50x + 15000)

=> - 0.000001x^3 - 0.01x^2 + 100x - 15,000

c) P(1900) = - 0.000001*(1900)^3 - 0.01*(1900)^2 + 100(1900) - 15000 = $132041

Hence the profit will be $132041

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