Q. We are selling ticket for a flight from HK to Shanghai. Our plane has 150 seats also we know which during the weekend we can sell all tickets however because of last minute cancellation our plane may depart with several empty seats. To cope with this issue, managers are considering overbooking policy which means to sell more than 150 seats to customers. Suppose which regular price for one seat for departure on Saturday is $220. If customer cancels his/her reserved seat, we would charge him/her 20% of the regular fare. In the case which more passengers than 150 available seats describe how on the day of departure, we will give a ticket with the value of $500 to passengers who could not board on the plane (still you charge them $220). Distribution of the number of no-shows is given in the subsequent table. Elucidate what is the optimal number of overbooked seats?

No. of no-shows Cumulative Probability
1 0.02
2 0.07
3 0.16
4 0.31
5 0.50
6 0.69
7 0.84
8 0.93
9 0.98
10 1.00