Linear Programming: Sundown Rent-A-Car

1. Management of Sundown Rent-a-Car (see Problem 8-8) has decided that perhaps the cost during the six-month period is not the appropriate Cost to minimize because the agency may still be obligated to additional months on some leases after that time. For example, if Sundown had some cars delivered at the beginning of the sixth month, Sundown would still he obligated for two additional months on a three-month lease. 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 entire life of these leases.
Problem 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:
Month March April May June July August
Demand 420 400 430 460 470 440

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 on each of the three types of leases are $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?