JetRed Airways flies several daily flights from Philadelphia to Chicago. Based on historical data, the flight on Wednesday evening before Thanksgiving is always sold-out. However, there are usually no-shows so the airline decides to improve revenues by overbooking. The no-shows are Poisson-distributed with mean 8 and the airline estimates that the cost of bumping a passenger is about 10 times more than ticket price. Suppose 6 seats are overbooked. How many seats can JetRed expect to have empty, on average (find the expect loss sales)? Solution Let be X the random variable that represents the number of empty seats. Let be Y the random variable that represents the number of no-shows. Let be C(X) the cost of X empty seats. Let be p the price of a ticket. Let be V the number of over-booked seats. V=6 X=Y-V E(X)=E(Y)-E(V) E(X)=8-6=2 empty setas expected C(X) =10*p*E(X)=20*p The cost is expected to be twenty times the price of a ticket seat. E(Y)=8 M-N=6 E(X)=E.

1. JetRed Airways flies several daily flights from Philadelphia to Chicago. Based on historical data,
the flight on Wednesday evening before Thanksgiving is always sold-out. However, there are
usually no-shows so the airline decides to improve revenues by overbooking. The no-shows are
Poisson-distributed with mean 8 and the airline estimates that the cost of bumping a passenger is
about 10 times more than ticket price. Suppose 6 seats are overbooked. How many seats can
JetRed expect to have empty, on average (find the expect loss sales)?
Solution
Let be X the random variable that represents the number of empty seats.
Let be Y the random variable that represents the number of no-shows.
Let be C(X) the cost of X empty seats.
Let be p the price of a ticket.
Let be V the number of over-booked seats.
V=6
X=Y-V
E(X)=E(Y)-E(V)
E(X)=8-6=2 empty setas expected
C(X) =10*p*E(X)=20*p
The cost is expected to be twenty times the price of a ticket seat.
E(Y)=8
M-N=6
E(X)=E