$8-8($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 Demand March $420$ April $400$ May $430$ June $460$ July $470$ August $440$

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