Assume each plant can produce only up to 200 gallons. (a) Set up the problem for each plant, and determine production, pollution (smog) and damage when there is no policy. (b) Set up the problem for each plant, and determine production, pollution (smog) and damage that maximizes welfare. (Hint: to solve it, imagine each plant faces private costs plus social costs of production). (c) Set up the problem for each plant, and determine production when a pigouvian tax is imposed