2.7 Production Planning for Automobiles: The Auto Company of America (ACA) produces four types of cars: subcompact, compact, intermediate, and luxury. ACA also produces trucks and vans. Vendor capacities limit total pro- duction capacity to at most 1,200,000 vehicles per year. Subcompacts and com- pacts 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 capacity of 400,000; and the truck/van facility has a capacity of 275,000. ACA's marketing strategy requires that subcompacts and compacts must constitute at least half of the product mix for the four car types. Profit margins, market potential, and fuel efficiencies are summarized below. Profit Margin Type ($/Vehicle) Potential Sales (in 000s) Fuel Efficiency (MPG) Subcompact 150 600 40 Compact 225 400 34 Intermediate 250 300 15 Luxury 500 225 12 Truck 400 325 20 Van 200 100 25 The Corporate Average Fuel Efficiency (CAFE) standards require an average fleet fuel efficiency of at least 27 MPG. ACA would like to use a linear program- ming model to understand the implications of government and corporate policies on its production plans./n61 (a) What is the optimal annual profit for ACA? (b) How much would the annual profit drop if the fuel efficiency requirement were raised to 28 MPG?

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