An automobile manufacturing company produces three lines of cars: Sub-Compact, Compact, and Mid-Sized, with fuel efficiency ratings of 32, 24, and 17 miles per gallon. It must produce at least 100,000 cars in the coming year and in order to satisfy federal environmental legislation the average fuel efficiency rating of cars produced must be at least 25 miles per gallon. Because of the high profit margin, the company would like to produce at least 25,000 Mid-Sized cars. The capacity of their engine plant for the smaller models limits production of Sub-Compacts and Compacts to a total of 90,000. The current MSRP prices of the three types of cars are $14,500, $19,000, and $23,000 for the Sub-Compact, Compact, and Mid-Sized, respectively. Most cars are expected to sell at these MSRP prices, but based on past experience the company expects that 10% of the Sub-Compacts and Compacts produced will have to be sold at a 15% discount and that 20% of the Mid-Sized cars will have to be sold at a 20% discount.
Formulate an LP for this problem that can be used to maximize the company’s sales revenue.