A company builds sport utility vehicles, trucks, and cars. The amount of steel needed for each of these vehicles as well as the miles per gallon for each is given in the accompanying tables.

The company wants to determine a manufacturing schedule for the next 3 months for each vehicle. Steel cost, as well as the maximum available steel for each month, is shown in an accompanying table. If steel is purchased in a certain month, it must be used in that month.

Demand for sport utility vehicles (SUVs), trucks, and cars as well as beginning inventories of each vehicle are shown in an accompanying table. Vehicles that are not sold in month 1 can be held and then sold in month 2 to meet month 2 demand. Likewise, vehicles that are not sold in month 2 can be held and then sold in month 3 to meet month 3 demand. If a vehicle is held from one month to the next, a $150 holding cost will be incurred.

Due to federal government regulations, all units manufactured in a particular month should average a minimum of 20 mpg fuel economy.

You should determine how to minimize the total cost (production + inventory cost) while meeting demands and staying within the requirements of available material (steel), production limits, and a gas milage considerations. Use a linear programming model showing all work in excel.

	Steel Req'd per vehicle	MPG
cars	1	25
Trucks	3	25		Holding Cost per vehicle	$ 150
SUVs	2	30
				Monthy Average MPG req'd	20
	Beginning Inventory (to start Month 1)
cars	15				Month 1	Month 2	Month 3
Trucks	15			Steel Cost	$ 700	$ 850	$ 900
SUVs	5			Max Available Steel (tons)	175	175	175
Max Production	100	vehicles per month
Demands	Month 1	Month 2	Month 3
cars	50	35	40
Trucks	10	25	20
SUVs	35	20	45