The Cost of Controlling Emissions at a Firm Goes Up $C ( q ) = 2,500 + 200 q ^ { 2 }$

Multiple Choice

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model: $C ( q ) = 2,500 + 200 q ^ { 2 }$
Where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. Government clean-air subsidies to the firm are based on the formula
$S ( q ) = 800 q$
Where q is again the reduction in emissions (in pounds per day) and S is the subsidy (in dollars) . Calculate the net cost function
$N ( q ) = C ( q ) - S ( q )$
Given the cost and subsidy above, and find the value of q that gives the lowest net cost. What is this lowest net cost

A) $q = \$ 2 , N ( q ) = \$ 3,400$
B) $q = \$ 2 , N ( q ) = \$ 1,700$
C) $q = \$ 2.5 , N ( q ) = \$ 1,700$
D) $q = \$ 4 , N ( q ) = \$ 1,700$
E) $q = \$ 2.5 , N ( q ) = \$ 1,750$