Delta Airlines 5430 is a non-stop flight from Detroit, MI to Cleveland, OH. Ther

Question

Delta Airlines 5430 is a non-stop flight from Detroit, MI to Cleveland, OH. There are 44 seats on the plane. The one-way standard fair is $280, but with a 21-day advanced purchase, customers can purchase a ticket at for a price of $100. If there is any unsold ticket on the night before the flight departs, Delta can sell the seat to someone on Priceline.com at a price of $40. Suppose the demand for the early purchase option exceeds the flight capacity and that the standard fare customers' demand for every DL 5430 flight can take any value from 1, 2, 3, .., 25 with equal probability. a) What is the expected number of standard fare customers? b) In order to maximize expected revenue for the DL 5430 flight, how many seats should be reserved for the standard fare customers? Find the optimal value using the critical ratio approach. Using your answer from part (b), what is the daily expected revenue for the 4682 flight if you reserve the optimal number of seats for standard fare customers? c)

Explanation / Answer

Our understanding of the passage is demand for early purchase option is infinite which means any ticket put on sale for early purchase option will definitely be taken. Now we just have to estimate how much should be put for early purchase option so that we don’t have a case of empty seat in the end which we would have to sell for $40.

Now its is given that the customer demand for values 1,2,3,4… 25 is of equal probabilities which would be 100/25 i.e 4% and for demand of 26,27,…44 seats, the probability is ZERO which means we are certain that the standard fare customers would never be 26 or more.

Expected number of standard fare passengers.

Since the demand for standard seats is distribution with equal probabilities from values 1 to 25, it is a normal distribution thus we can safely deduce that the demand i.e mean value would be at mid way of the curve i.e 13 seats (12.5 rounded up).

Using the critical ratio method we would try to find the number of seats to be reserved for standard value tickets.

Crtitical ratio = (Standard Price – Early purchase price )/(Standard Price – priceline.com price )

= (280-100)/(280-40)

= 75%

Hence we would assume the demand for standard prices seats to be qual to that when the cumulative probability matches 75% which would be at 19 seats (19 * 4% is just greater than 75%)

Daily Optimal revenue would be 19*280+(44-19)*100 =$7820

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