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 accomanying tables.

The company wants to determine a manufacturing schedule for the next three 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), trukcs and cars (XOs) as well as beginning inventories of each vehcile are shown in an accompanying table. (All demand must be met.) 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 holding cost of $190 (per month per vehicle) will be incurred.

Due to federal goverment regulations, all units manufactured in a particular month should average a minimum 17 mpg fuel economy.

To make sure complete vehicles are made, a constraint to prevent partial values should be used. (That is, the solution should be integers.)

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 gas mileage considerations. Use a linear programming model showing all work in Excel.

Hint: Be sure to avoid non-linearities that might arise if you divide decision variables into other decision variables.

Steel Req'd per vehicle MPG Cars 20 Trucks 12 Holding Cost per vehicle S 190 SUVS N 17 Monthy Average MPG req'd 17 Beginning Inventory (to start Month 1) Cars 10 Month 1 Month 2 Month 3 Trucks 15 Production Steel Cost S 700 $ 790 $ 845 SUVS Max Available Steel (tons) 175 175 175 Max Production 100 vehicles per month Demands Month 1 Month 2 Month 3 Cars 60 40 40 Trucks 20 31 25 SUVS 40 20 45