Suppose you have three production facilities that are polluting a river. Each emits 20 units of pollution. Their marginal cost functions for reducing emissions are, respectively, MC1 = $6, MC2 = $8, MC3 = $10. a) If the objective is to cut emissions to a total of 30 units cost-effectively via a command & control type policy approach, how much reduction should be assigned by the regulatory authority to each firm? Show your work. b) What would be the total variable cost of controlling these emissions? (You may want to start by defining what total variable cost is.) c) What would be the total variable cost that would result from forcing each facility to control one-half of it emissions? Is this different from the cost associated with the cost-effective allocation? Why or why not?