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 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 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. The Corporate Average Fuel Economy (CAFE) standards in the Energy Policy and Conservation Act require an average fleet fuel economy of at least 27 mpg.
Profit margins, market potential, and fuel efficiencies are summarized as follows:

a. What is the optimal profit for ACA?
b. What is the pattern in the optimal allocation?
c. How much would optimal annual profits drop if the fuel economy requirement were raised to 28 mpg?

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Fuel Profit Margin ($/vehicle) Market Potential Economy (mpg) Type (sales in '000) Subcompact 150 600 40 Compact 225 400 34 Intermediate 250 300 15 Luxury 500 225 12 Truck 400 325 20 Van 200 100 25