Operations problem

 

“India Go” Airlines runs a daily flight from Mumbai to Los Angeles with an Airbus A380 accommodating about 500 passengers. Since introduction, the airline observed that a sizeable chunk of ticket holders cancel their reservations in the last minute. So, the company intentionally overbooks the flight. Cancellations can be approximated by a normal distribution with 25 passengers corresponding to 50th percentile with a variance of 10.24 passengers. Profit per passenger is $200. If a passenger arrives but cannot board due to overbooking, the company’s policy is to provide cash payment of $400. How many tickets should be overbooked to maximize expected profit?

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