During the next two months General Cars must meet (on time) the following demands for trucks and cars: month 1, 400 trucks and 800 cars; month 2, 300 trucks and 300 cars. During each month at most 1000 vehicles can be produced. Each truck uses 2 tons of steel, and each car uses 1 ton of steel. During month 1, steel costs $400 per ton; during month 2 steel costs $600 per ton. At most 2500 tons of steel can be purchased each month. (Steel can be used only in the month in which it is purchased.) At the beginning of month 1, 100 trucks and 200 cars are in the inventory. At the end of each month, a holding cost of $150 per unsold vehicle is assessed. Determine how to meet the demand requirement at minimum total cost. (You may assume that steel is the only input in production)

(a) Define the decision variables. 

(b) State the objective (as a function of the inputs specified in the problem, the decision variables defined in (a), and/or any clearly defined intermediate variables).

(c) State the constraints. (These must be based on the inputs specified in the problem, the decision variables defined in (a), and/or intermediate variables.) Clearly identify each constraint with a meaningful label.

(d) Implement the model using Solver. What is the optimal solution (i.e. decision variables as well as the cost amount)?

(e) Conduct a sensitivity analysis.

Interpret the shadow price of the constraint that only 1000 vehicles can be produced in each month.

Please attach the sensitivity report and excel file to this tutor request.