Reference no: EM132471579

Point 1: 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.

Point 2: The manufacturer must determine a production plan for these three types of vehicles for each of the next three months. In Month 1, steel is expected to cost $700 per ton. In Month 2, steel is expected to cost $800. In Month 3, steel is expected to cost $850 per ton. Steel must be used in the month is is purchased. A maximum of 175 tons of steel is available for purchase each month.

Point 3: At the beginning of Month 1 there 15 Cars, 15 Trucks and 0 SUVs in inventory. In Month 1, there is a demand for 60 Cars, 20 Trucks and 40 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 40 Cars, 30 Trucks, and 20 SUVs. Any vehicles remaining after meeting demand in Month 2 can be used to meet demand in Month 3, at an inventory cost of $200 per vehicle. In Month 3, there is a demand for 40 cars, 25 Trucks, and 45 SUVs. A maximum of 100 vehicles may be produced in a single month.

Point 4: Industry standards require that the average gas mileage of all vehicles produced in a given month should be at least 17 mpg.

Point 5: Only whole vehicles can be sold, so use a constraint to prevent fractional values in your solution.

Question 1: 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.