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 tons/day)C (2 tons/day)D (1 ton/day)E (0 tons/day)
Cost to Sludge Oil ($/day)5070120200500
Cost to Northwest Lumber ($/day)1001805001,0002,000

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.

How much will each permit sell for in this auction?