Chapter 1.2, Problem 43E

Toxic Waste Treatment The cost of treating waste by removing PCPs goes up rapidly as the quantity of PCPs removed goes up. Here is a possible model:

$C\left(q\right)=2,000+100q^2$, where q is the reduction in toxicity (in pounds of PCPs removed per day) and $C\left(q\right)$ is the daily cost (in dollars) of this reduction.

a. Find the cost of removing 10 pounds of PCPs per day.

b. Government subsidies for toxic waste cleanup amount to

$S\left(q\right)=500q$

where q is as above and $S\left(q\right)$ is the daily dollar subsidy. The net cost function is given by $N=C-S$. Give a formula for $N\left(q\right)$, and interpret your answer.

c. For $N\left(20\right)$, and interpret your answer.