In July 1997, the EPA announced new air quality standards for small (2.5 micrometers in diameter) particulate matter referred to as PM-2.5. Steel mills are a major source of these smaller particles and therefore must find ways to abate. To analyze the implications, consider the following hypothetical model of two steel plants, one owned by Bethlehem Steel (B) and one by National Steel (N), both located in Pittsburgh, Pennsylvania: 

Bethlehem: .............MAC_B   = 1.2A_B

.................................TAC_B   = 0.6A_B²  

National:....................MAC_N = 0.3A_N

_{............................................}TAC_N = 0.15A_N ²

Assume that each plant emits 40 units of PM-2.5 for a total of 80 units. In order for the Pittsburgh area to meet the new standard, the EPA determines that the combined abatement for both plants must total 30 units.

a. Assuming the new abatement standard is implemented uniformly across the two firms, find the total cost of abatement.

b. Find the cost-effective solution and illustrate graphically, labeling all curves, intercepts, and relevant intersections. Calculate the associated cost savings.