There are three petrochemical plants, A, B, and C, in Houston, Texas. The three plants produce Good Stuff. Unfortunately, they also dump Bad Stuff into Houston air. Data concerning their outputs of Stuff are shown below: OutputsGood (kg/day) Bad/Good (cL/kg)Plant A 17,000 10Plant B 11,000 15Plant C 8,000 18The city wants to reduce the dumping of Bad Stuff by 150 centilitres per day. Costs for reducing the concentration of Bad Stuff in output are shown below.The city is considering two methods:

(1) Require all plants to meet the performance level of the bestpractice plant, plant A, which is 10 centilitres of Bad Stuff per kilogram of Good Stuff.

(2) Impose a tax of $0.20/centilitre of Bad Stuff dumped.Incremental Cost of Reducing Bad Stuff/Good Stuff ($/cL/kg)Reduction (cL/kg)1 2 3 4 5 6 7 8Plant A 0.02 0.032 0.048 0.1 0.18 0.26 0.38 0.57Plant B 0.06 0.06 0.063 0.068 0.075 0.193 0.27 0.405Plant C 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.375

(a) What will be the reduction in dumping of Bad Stuff under the best-practice regulations? What will be the cost of this reduction?

(b) Under the tax, how much Bad Stuff will be dumped from the three plants combined? What will be each plant's reduction in dumping per kilogram of Good Stuff?

(c) How much will the reduction of dumping cost for each company be under the tax?