Question

South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 27 passengers, and the airline makes a $98 profit on each passenger on the flight. When South Central takes 25 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 27 reservations, South Central is averaging 25 passengers with a profit of 25(98) = $2,450 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 29 reservations even though the airplane holds only 27 passengers. The probability distribution for the number of passengers showing up when 29 reservations are accepted is as follows:

Passenger Showing Up	Probability
25	0.05
26	0.25
27	0.50
28	0.15
29	0.05

The airline will receive a profit of $98 for each passenger on the flight, up to the capacity of 27 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 $130 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.

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

Over $ = ?

Values for RAND()

0.7346

0.8378

0.8956

0.0441

0.4378

0.4604

0.0718

0.3930

0.4445

0.7211

0.1036

0.0617

0.0801

0.6012

0.1322

0.3333

0.8035

0.7896

0.4370

0.0231

0.2353

0.1021

0.5164

0.0907

0.2147

0.8732

0.8408

0.7182

0.5756

0.8693

0.2486

0.7249

0.5410

0.0816

0.1111

0.0006

0.4044

0.7609

0.9636

0.7910

0.2083

0.6918

0.3680

0.1092

0.1961

0.7305

0.5340

0.3901

0.0638

0.7303

0.0931

0.2691

0.0790

0.9540

0.9784

Answer 1

----------------------------

Values for RAND()	Passenger Showing Up	Seat given	Denied	Profit for seat given	Cost for denied	Net profit		Average net profit		Cumulative	Passenger Showing Up	Probability
0.7346	27	27	0	$2,646	$0	$2,646		$2,581		0.00	25	0.05
0.8378	28	27	1	$2,646	$130	$2,516				0.05	26	0.25
0.8956	28	27	1	$2,646	$130	$2,516				0.30	27	0.50
0.0441	25	25	0	$2,450	$0	$2,450				0.80	28	0.15
0.4378	27	27	0	$2,646	$0	$2,646				0.95	29	0.05
0.4604	27	27	0	$2,646	$0	$2,646
0.0718	26	26	0	$2,548	$0	$2,548
0.393	27	27	0	$2,646	$0	$2,646
0.4445	27	27	0	$2,646	$0	$2,646

The mean profit per flight is coming as $2,581.