A regional airline \"Jimmy\'s Island Hoppers\" operates a 50 seat jet with price

Question

A regional airline "Jimmy's Island Hoppers" operates a 50 seat jet with prices at $600 per seat. If the airline overbooks and more than 50 show up overbooked passengers receive a SI000 travel voucher. The airline has overbooked up to 52 seats in the past. For this particular day the airline is considering overbooking up to 2 passengers. Based on past tendencies for this day the airline has probabilities charted above for each scenario. Based on these probabilities how many people should the airline book?

Explanation / Answer

If the airlines books 50 seats

it will have a profit = 600 * (0.23 *45 + 0.2 *46 + 0.15 *47 +0.22 *48 + 0.15 * 49 + 0.05 *50)

Profit = 49134

.

If 51 seats are booked:

Profit = 600*(0.22*45+0.13*46+0.13*47+0.1*48+0.28*49+0.1*50+0.04*50) + (600-1000)*0.04

The Profit = 28490

.

If 52 seats are booked:

Profit = 600*(0.07*45+0.105*46+0.175*47+0.23*48+0.35*49+0.05*50+0.01*50+0.01*50) + (600-1000)*0.01+(600-1000)*0.01*2

Profit = 28725

.

Thus we can see that the airlines is profitable only when it books 50 tickets.

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