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# Business Calculus and Average Cost Function

1. Average Cost. A company manufacturing snowboards has fixed cost of \$200 per day and total cost of \$3800 per day at a daily outputs of 20 boards.

a) Assuming that the total cost per day c(x) is linearly related to the total output per day x, write an equation for the cost function.
b) The average Cost per board for an output of x boards is given by c(x)=C(x)/x. find the average cost function.
c) Sketch a graph of the average cost function, including any asymptotes, for 1 less than or equal to x less than or equal to 30.
d) What does the average cost per board tend to as production increases?

2. Pollution. In Silicon Valley (California), a number of computer related manufacturing firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and to contribute to a monetary pool for testing and cleanup of the underground contamination. suppose that the required monetary pool (in millions of dollars) for the testing and cleanup is estimated to be given by
P(x)=2x/1-x 0 less than or equal to x less than 1
where x is the percentage (expressed as a decimal fraction) of the total contaminant removed.

a) How much must be in the pool to remove 90% of the contaminant?
b) How much must be in the pool the remove 95% of the contaminant?
c) Find lim x approch 1- P(x) and discuss the implications of this limit.

#### Solution Preview

Dear student, please refer to the attachment for full solutions.
a)
Total Cost per day = \$3800
Fixed Cost per day = \$200
Variable Cost ...

#### Solution Summary

Business calculus and average cost functions are examined. The average cost per board tend to as production increases are given.

\$2.19