1. Cost Benefit Model

Question

Environmental scientists often use cost-benefit models to estimate the cost of removing a pollutant from the environment as a function of the percentage of pollutant removed. Suppose a cost benefit function for the cost C (in millions of dollars) of removing x percent of the pollutants from Maple Lake is given by

C(x)= 25x/100-x


a. Find the domain and interpret what it means within the text.

b. If federal government wants to remove 90% of the pollutants, how much should the budget be ?

c. If federal government budgets $100 million to clean up the lake, what percent of the pollutants can be removed?

d. If federal government budgets $225 million to clean up the lake, what percent of the pollutants can be removed?

Answer 1

The domain would be any positive value of x < 100
(at x=100 or to completely remove the pollutants, we would be dividing by zero, which is undefined)

a) to remove 90% , let x = 90
C(90) = 25(90)/(100-90) = 225

b) 100 = 25x/(100-x)
10000-100x = 25x
125x = 10000
x = 80

c) wasn't that the answer from a) , so .....