Universal Aviation currently is investigating the possibility of branching out from its passenger service into the small-plane air-freight business. With $4,000,000 available to invest in the purchase of new twin-engined cargo aircraft, Universal is considering three types of planes. Aircraft A, costing $80,000, has a ten-ton payload and is expected to cruise at 350 knots, while airplane B can haul 20 tons of goods at an average speed of 300 knots. Aircraft B will cost $130,000. The third aircraft is a modified form of B with provisions for a copilot, a 300-knot cruising speed, a reduced capacity of 18 tons, and a cost of $150,000.
Plane A requires one pilot and, if flown for three shifts, could average 18 hours a day in the air, as could aircraft B. While transports B and C both require a crew of two, C could average 21 hours of flying per day on a three-shift pilot basis due to superior loading equipment. Universal's operations department currently estimates that 150 pilot-shifts will be available for each day's cargo operations. Limitations on maintenance facilities indicate that no more than thirty planes can be purchased. The contributions of planes A, B, and C per ton-mile are, respectively, $1, $8, and $120. 3,500,000 ton-miles of shipping must be completed each day, but deliveries not completed by the in-house fleet can still be sub-contracted to outside air carriers at a contribution of $0.20 per ton mile. What ‘‘mix'' of aircraft should be purchased if the company desires to maximize its contribution per day? (Note. Consider a knot = 1 mile/hour.)