We are selling ticket for a flight from HK to Shanghai. Our plane has 150 seats and we know that…

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We are selling ticket for a flight from HK to Shanghai. Our plane has 150 seats and we know that during the weekend we can sell all tickets but 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. Assume that 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 that more passengers than 150 available seats show up on the day of departure, we will provide 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 following table. What is the optimal number of overbooked seats?

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