Chapter 1.2, Problem 43E

(a)

To determine

To calculate: The cost of removing $10$ pounds of PCPs per day, if the model of the cost treating waste by removing PCPs is $C\left(q\right)=2000+100q^2$, where q is the reduction in toxicity (in pounds of PCPs removed per day) and $C\left(q\right)$ is the cost of reduction per day in dollars that goes up rapidly as the quantity of PCPs removed goes up.

(b)

To determine

The formula for $N\left(q\right)$ where net cost function is provided by $N=C-S$, if the model of the cost treating waste by removing PCPs is $C\left(q\right)=2000+100q^2$, where q is the reduction in toxicity (in pounds of PCPs removed per day) and $C\left(q\right)$ is the cost of reduction per day in dollars that goes up rapidly as the quantity of PCPs removed goes up and the government subsidies for toxic waste cleanup amount to $S\left(q\right)=500q$, where, $S\left(q\right)$ is the subsidy per day in dollars.

(c)

To determine

To calculate: The value of $N\left(20\right)$, if the model of the cost treating waste by removing PCPs is $C\left(q\right)=2000+100q^2$, where, q is the reduction in toxicity (in pounds of PCPs removed per day) and $C\left(q\right)$ is the cost of reduction per day in dollars that goes up rapidly as the quantity of PCPs removed goes up and the government subsidies for toxic waste cleanup amount to $S\left(q\right)=500q$ where, $S\left(q\right)$ is the subsidy per day in dollars.