Offwego Airlines has a daily flight from Chicago to Las Vegas. On average, 18 ticket holders cancel their reservations, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a mean of 18 passengers and a standard deviation of 4.55 passengers. Profit per passenger is $ 99. If a passenger arrives but cannot board due to overbooking, the company policy is to provide a cash payment of $ 200. How many tickets should be overbooked to maximize expected profit?
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