Two firms, Sludge Oil and Northwest Lumber, have access to five production processes, each one of which has a different cost and gives off a different amount of pollution. The daily costs of the processes and the corresponding number of tons of smoke emitted are as shown in the following table: Process (smoke) A (4 tons/day) B (3 C (2 D (1) E (0
ton/day ton/day ton/day tons/day)

Cost to Sludge Oil ($/day) 50 70 120 200 500
Cost to Northwest Lumber ($/day) 100 180 500 1,000 2,000
The City Council wants to curb emissions by half and decides to auction off four permits, each of which entitles the bearer to emit 1 ton of smoke per day. No smoke may be emitted without a permit. Suppose the government conducts the auction by starting at $1 and asking how many permits each firm wants to buy at that price. If the total is more than four, it then raises the price by $1 and asks again, and so on, until the total quantity of demanded permits falls to four.
1. How much will each permit sell for in this auction?
2. How many permits will each firm buy?
3. What will be the total cost to society of this reduction in pollution?