The Cost of Controlling Emissions at a Firm Goes Up $C ( x , y ) = 6,000 + 200 x ^ { 2 } + 75 y ^ { 2 }$

question 125

Essay

The cost of controlling emissions at a firm goes up rapidly as the amount of emissions reduced goes up. Here is a possible model.
$C ( x , y ) = 6,000 + 200 x ^ { 2 } + 75 y ^ { 2 }$
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 $300 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)

Enter your answer as an ordered pair in the form $( x , y )$ . Round your answer to three decimal places if necessary.

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Definitions:

Amount of Supply

The total quantity of a particular good or service available for purchase at any given time.

Nonrenewable Sources

Energy sources that cannot be replenished in a short period, such as coal, oil, and natural gas.

Renewable Sources

Energy sources that are replenished naturally and sustainably, such as wind, solar, and hydroelectric power.

Transitional Expression

Phrases or words used to link sentences and paragraphs smoothly, helping to signal connections between ideas.