The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model:
$C ( q ) = 3,500 + 150 q ^ { 2 }$
Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. Government clean air subsidies amount to $750 per pound of pollutant removed. How many pounds of pollutant should the firm remove each day to minimize net cost (cost minus subsidy)

A)2 pounds
B) 10 pounds
C) 2.5 pounds
D) 5 pounds
E) 75 pounds

Question

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: 
 $C ( q ) = 3,500 + 150 q ^ { 2 }$ 
Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. Government clean air subsidies amount to $750 per pound of pollutant removed. How many pounds of pollutant should the firm remove each day to minimize net cost (cost minus subsidy) 
 
A)2 pounds
B) 10 pounds
C) 2.5 pounds
D) 5 pounds
E) 75 pounds

Quizplus · Accepted Answer

The net cost is given by $N(q) = C(q) - 750q = 3,500 + 150q^2 - 750q$$\frac{dN}{dq} = 300q - 750$Setting the derivative equal to zero and solving for q gives:$300q - 750 = 0$$q = 2.5$Therefore, the firm should remove 2.5 pounds of pollutant each day to minimize net cost.

The Cost of Controlling Emissions at a Firm Goes Up C(q)=3,500+150q2C ( q ) = 3,500 + 150 q ^ { 2 }C(q)=3,500+150q2

The Cost of Controlling Emissions at a Firm Goes Up $C ( q ) = 3,500 + 150 q ^ { 2 }$