Question

South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 30 passengers, and the airline makes a $100 profit on each passenger on the flight. When South Central takes 28 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 30 reservations, South Central is averaging 28 passengers with a profit of 28(100) = $2,800 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 32 reservations even though the airplane holds only 30 passengers. The probability distribution for the number of passengers showing up when 32 reservations are accepted is as follows:

Passenger Showing Up	Probability
28	0.05
29	0.25
30	0.50
31	0.15
32	0.05

The airline will receive a profit of $100 for each passenger on the flight, up to the capacity of 30 passengers. The airline will also incur a cost for any passenger denied seating on the flight. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $150 per passenger. Develop a worksheet model that will simulate the performance of the overbooking system. Simulate the number of passengers showing up for each of 500 flights by using the VLOOKUP function. Use the results to compute the profit for each flight.

A. What is the mean profit per flight if overbooking is implemented? Round your answer to the nearest dollar.

Over $   

Answer 1

		Passanger turning up	Profit
		28	$2,800	(28*100)
		29	$2,900	(29*100)
		30	$3,000	(30*100)
		31	$2,850	(3000-150)
		32	$2,700	(3000-(2*150)
		Pasanger showing up	Profit	Probability	Cumulative	Mapped
					Probability	Random No.
		28	$2,800	0.05	0.05	00-04
		29	$2,900	0.25	0.30	05.-29
		30	$3,000	0.50	0.80	30-79
		31	$2,850	0.15	0.95	80-94
		32	$2,700	0.05	1.00	95-99
		Using "RANDBETWEEN "Function
			Random Number	PassangersShowing up	Profit
			13	29	$2,900
			61	30	$3,000
			85	31	$2,850
			98	32	$2,700
			79	30	$3,000
			36	30	$3,000
			14	29	$2,900
			28	29	$2,800
			82	31	$2,850
			8	29	$2,900
			61	30	$3,000
			35	30	$3,000
				Total	$34,900
				Average	$2,908.33	(34900/12)
			MEAN PROFIT PER FLIGHT	$2,908