Chapter 5.1, Problem 83E

Production costs. The graph of the marginal cost function from the production of x thousand bottles of sunscreen per month [where cost C(x) is in thousands of dollars per month] is given in the figure.

1. (A) Using the graph shown, describe the shape of the graph of the cost function C(x) as x increases from 0 to 8,000 bottles per month.
2. (B) Given the equation of the marginal cost function.

     $C^{\prime }\left(x\right)=3x^2-24x+53$

find the cost function if monthly fixed costs at 0 output are $80,000. What is the cost of manufacturing 4,000 bottles per month? 8,000 bottles per month?

(C)    Graph the cost function for $0\le x\le 8$. [Check the shape of the graph relative to the analysis in part (A).]