Amtrak is trying to decide whether or not to overbook the first class cabins on its most popular daily commuter routes from DC to NY. In doing so, Amtrak is seeking to get the most from its business customers.
The operations department have done some preliminary research and have determined the following:
On average, the frequency of no-shows is
Number of N-Shows / Freq.
0 / 5
1 / 7
2 / 5
3 / 3
Any Amtrak business customer who has a ticket but is denied the opportunity to board (because of oversold trip), receives a refund of $500 (cost of the ticket) and $600 in cash.
Any Amtrak business customer who has a ticket but chooses not to show up to board, loses the ticket and the money he/she paid for the ticket. In essence, they receive nothing.
Suppose the first class cabin has 250 seats.
1. Calculate what the optimal number of reservations Amtrak should accept should be
2. If the optimal number of reservations listed in part 1 is implemented, calculate what the expected value of "loss sales" per trip would be
3. If the government makes it illegal to overbook trips, calculate what the expected loss (relative to the optimal number of reservations listed in part 1) per trip would be