The Beta Corporation has just purchased an existing franchise operation for the limousine service between the DFW Airport and the downtown area. Previously, the limo service had operated a fleet of 30 station wagons; however, the volume of business is such that additional vehicles could easily be justified. In addition, most of the vehicles are very old and require heavy maintenance. Because of the small investment required in the purchase of the franchise, Beta is in a position to replace all existing vehicles. Three types of vehicles are under consideration: station wagons, minibuses, and large buses. The company has examined each type of vehicle and collected the following data:

The board of directors at Beta has authorized $500,000 for the purchase of vehicles. Beta has projected that it can adequately employ as many vehicles as it can afford to put into the fleet; however, the service and maintenance facilities are limited. Currently, the maintenance department can handle 30 station wagons. At the present time the company does not wish to expand the maintenance facilities. Since the new fleet may contain minibuses and large buses, the maintenance department must be able to handle these. A minibus is equivalent to 1.5 station wagons and each large bus is equivalent to 3 station wagons. Beta wishes to determine the optimum number of each type of vehicle to purchase in order to maximize expected annual profits.

Vehicle Type Station wagon Minibus Purchase Price $16,500 20,500 39,000 Expected Annual Net Profit (per vehicle) $3,000 3,800 6,500 Large bus Vehicle Type Station wagon Minibus Purchase Price $16,500 20,500 39,000 Expected Annual Net Profit (per vehicle) $3,000 3,800 6,500 Large bus