The Cost of Controlling Emissions at a Firm Goes Up $C ( x , y ) = 6,000 + 100 x ^ { 2 } + 25 y ^ { 2 }$

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. $C ( x , y ) = 6,000 + 100 x ^ { 2 } + 25 y ^ { 2 }$
Where x is the reduction in sulfur emissions, y is the reduction in lead 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 $600 per pound of sulfur and $50 per pound of lead removed. How many pounds of pollutant should the firm remove each day to minimize the net cost (cost minus subsidy)

A) 3.5 lb of sulfur and 2 lb of lead
B) 6 lb of sulfur and 1 lb of lead
C) 3 lb of sulfur and 1 lb of lead
D) 1.9 lb of sulfur and 3.5 lb of lead
E) 1 lb of sulfur and 3 lb of lead