The flight from Philadelphia to Chicago has 250 seats. The airline offers a high
ID: 470149 • Letter: T
Question
The flight from Philadelphia to Chicago has 250 seats. The airline offers a high and low fare. There is ample demand for the low fare. Low fare customers buy in advance of high fare customers. Demand for the high fare is normally distributed with a mean of 100 and a standard deviation of 40. The high fare is $700 and the low fare is $450.
What is the total expected revenue (including both low and high-fare passengers) when the protection level is 110 seats?
The number of no-shows on this flight has a Poisson distribution with mean of 9.5. The airline estimates the cost of bumping a passenger on this flight is $1500. What is the optimal maximum number of reservations to accept on this flight?
Explanation / Answer
Z = 110 seats (protection) -100 / 40 =0.25
z =0.25 is 0.2863
Expected Sales = Mean - Z * standard deviation
=100 - 0.2863 * 40
=100-11.45
=88.55
Total expected revenue = Hire Fare * Sales + Low fare *(AVail seat -Protection seat )
=$700 * 88.55 + $450.(250 - 110)
=$700 * 88.55 + $450(140)
=$61,985+63,000
=$124,985
____________________________________________________________________________
optimal maximum number of reservations = Marginal Benefit / Marginal Benefit +Marginal Cost
=$450 / 450 +1500
=$450 / $1950
=0.2307
from poission distribution table 0.2307 value taken is 7
maximum number of reservations = Reservations+ optimal
= 250+ 7
=257