1. (27 points) Drof Automobiles produces four types of cars: subcompact, compact, intermediate, and luxury. Drof also produces trucks and vans. Vendor capacities limit total production capacity to at most 1.2 million vehicles per year. Subcompacts and compacts are built together in a facility with a total annual capacity of 620,000 cars. Intermediate and luxury cars are produced in another facility with a total annual capacity of 400,000 ; and the truck/van facility has a total annual capacity of 275,000 . Profit margins, market potential (in terms of maximum sales), and fuel efficiencies are summarized as follows. Drof would like to determine the optimal vehicle mix so as to maximize profit. (In this problem do not worry about integer restrictions, it is okay if the solution contains a non-integer value in the production mix). (a) Write down a Linear Program (i.e., mathematical/algebraic) formulation for the above optimization problem. Make your formulation clear by defining the decision variables, constraints, objective function etc. clearly. (b) Implement and solve your linear programming model in Solver. Submit your Excel spreadsheet Solver Model for this part (i.e., the actual Excel file). (c) What is the optimal profit? State in words. (d) What is the optimal combination of vehicles to produce? State in words. (e) The US government has just passed legislation that requires the average fuel economy of the vehicles manufactured by an automobile manufacturer to be at least 28 miles per gallon. (Note. The legislation by itself does not eliminate any vehicle from being manufactured. It simply requires the average fuel economy taken over all vehicles manufactured by an automobile manufacturer to be at least 28 miles per gallon). Will this affect the current production plan? If so, i) explain mathematically how to modify your model, and ii) implement your modification (do this in a separate sheet containing its own Solver Model) to determine the new optimal profit and production plan. (To obtain full credit the modified model should be linear). Submit your Excel Spreadsheet Solver Model for this part (i.e., the actual Excel file) along with your answers