Assignment:
Q1. Average Cost. A company manufacturing snowboards has fixed cost of $200 per day and total cost of $3800 per day at a daily output 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, 1≤x≤30
D). What does the average cost per board tend to as production increases?
Q2. 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≤x≤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 and limx→1 p(x) discuss the implications of this limit.
Provide complete and step by step solution for the question and show calculations and use formulas.