Question

There are two coal-fired power plants located in the vicinity of a major metropolitan area. These power plants emit sulphur dioxide, which causes respiratory issues for the metro population as well as resulting in acidic rainfall.  The EPA has determined that the amount of sulphur dioxide emitted needs to be reduced by 180 tons. The marginal abatement cost function for the first power plant is given by MC(x) = 5x and the marginal abatement cost function for the second power plant is given by MC(y) = 7y, where x is the amount of emissions reduction done by the first power plant, and y is the amount of emissions reduction done by the second power plant.

In order to ensure that the target level of emissions reduction is achieved in the most cost-effective way, what should x be? Please round your answer to 2 decimal places.

Answer 1

Where equation says ,

5x +7y = 180(tons)

Assuming x = 0,

5(0) + 7y = 180

0+ 7y= 180

y = 180/7

y= 25.71.

Now taking y = 0

5x + 7(0) = 180

5x + 0= 180

5x = 180

x = 180/5

x = 36

Therefore the amount of emission reduction done by the first powerplant (x) = 36.0( rounding upto 2 decimals)