Cars Trucks SUVs Holding Cost pervehicle Monthly Ave MPG Req'd Steel Cost Max Available Steel (tons) Max Production Demands Cars Trucks SUVs Steel Req'd per vehicle 1 3 2 $200 1? Month 1 5700 17:5 100 Month 1 MPG 1? Month 2 1'35 100 Month 2 In itial Inventory 15 15 0 Month 3 135 100 Month 3 An automobile manufacturer makes three types of vehicles: Cars, Trucks, and SUVs. Each Car produced requires 1 ton of steel and gets 20 miles per gallon {mpg}. Each Truck requires 3 tons of steel and gets 12 mpg. Each SUV requires 2 tons of steel and gets 17 mpg. The manufacturer must determine a production plan for these three types of vehicles for each of the next three months. The expected cost of steel by month is given in an accompanying table along with the maximum steel available in that month and the max production quantity in that month. Steel must be used in the month it is purchased. Demand for each vehicle for each month is given in an accompanying table as well. All demand must be met on time. Beginning inventory of each vehicle is 15 Cars, 15 Trucks, and 0 SUVs and this inventory can be used to meet demand. Any vehicles remaining after meeting demand in any month is that month's ending inventory. For instance, assume that 50 cars are produced in month 1. lfthat 50 is combined with the 15 in initial inventory, then there is a total of 65 cars to meet month 1's demand of 60 units, leaving 5 units of inventory at the end of month 1. This 5 units can then be used to meet future demand. An inventory cost of $200 per vehicle is incurred for any endofmonth inventory for any vehicle. Given the car example above, this would be $1000 for cars for month 1. [Do not include any cost for the initial entering inventory only inventory left at the end of months 1, 2 and 3.) Industry standards require that the average gas mileage of all vehicles produced in a g'ven month should be at least 1? mpg. Only whole vehicles can be sold, so use a constraint to prevent fractional values in your solution