8-8 (Automobile leasing problem) Sundown Rent-a-Car, a large automobile rental agency operating in the Midwest, is preparing a leasing strategy for the next six months. Sundown leases cars from an automobile manufacturer and then rents them to the public on a daily basis. A forecast of the demand for Sundown's cars in the next six months follows:

Cars may be leased from the manufacturer for either three, four, or five months. These are leased on the first day of the month and are returned on the last day of the month. Every six months the automobile manufacturer is notified by Sundown about the number of cars needed during the next six months. The automobile manufacturer has stipulated that at least 50% of the cars leased during a six-month period must be on the five-month lease. The cost per month is $420 for the three-month lease, $400 for the four-month lease, and $370 for the five-month lease.

Currently, Sundown has 390 cars. The lease on 120 cars expires at the end of March. The lease on another 140 cars expires at the end of April, and the lease on the rest of these expires at the end of May.

Use LP to determine how many cars should be leased in each month on each type of lease to minimize the cost of leasing over the six-month period. How many cars are left at the end of August?

Demand for each month:

March 420

April 400

May 430

June 460

July 470

August 440