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 10 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 two months. In Month 1, steel is expected to cost $700 per ton. In Month 2, steel is expected to cost $800. Steel must be used in the month is is purchased. A maximum of 2500 tons of steel is available for purchase each month.
At the beginning of Month 1 there 200 Cars, 100 Trucks and 50 SUVs in inventory. In Month 1, there is a demand for 600 Cars, 200 Trucks and 400 SUVs. Any vehicles unsold in Month 1 may be used to meet demand in Month 2. Any vehicles remaining after meeting demand in Month 1 will be held in inventory at a cost of $200 per vehicle. In Month 2, there is a demand for 300 Cars, 300 Trucks, and 200 SUVs. A maximum of 1000 vehicles may be produced in a single month.
Industry standards require that the average gas mileage of all vehicles produced in a given month should be at least 16 mpg.
Build a linear programming model to 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 mileage considerations.
Please show the formulas and calculations used.