American Airlines flight to Hawaii has 61 seats left The ful

American Airlines flight to Hawaii has 61 seats left. The full-fare tickets are priced at $540 and the discount tickets are priced at $150. The airline estimates that the demand of full fare customers is between 31 and 70, all numbers equally likely.

Please show your work when solving the question, and if you can please try to solve it in excel. You can attach the excel file here, or you can email it to me pdxsneakerhead@gmail.com

For the 61th seat, should the airline sell one more discount ticket to  maximize the expected revenue?

How many seats should we reserve for the full fare class?

Solution

To maximize the expected revenue, should the airline sell one more discount ticket?

Let D be the probability that  the full-fare tickets demand.

If the airline holds the ticket, the probability the full-fare tickets demand is at least than 61

P(D 61) = (70 - 61 + 1) / (70 - 31 + 1) = 0.25

Holding the seat has an expected revenue of 540 * 0.25 = 135 < 150 ( discount ticket price)

How many seats should we reserve for the full fare class?

Let X be the number of seats left.

Reserve for full fare, or stop selling to discounted class when.

150 < 540 * P(D X)

150 / 540 < P(D X)

P(D X) 5/18

(70 - X + 1) / 40 5/18

(70 - X + 1) 200 / 18

71 - X   11.1111

71 - 11.1111   X

59.8889   X

X < 59.8889

The airline should reverse 60 seats for the full-fare class.