Problem 4 (Overbooking): Suppose you cannot charge latecomers a different rate because of a city ordinance that prohibits "price gouging" during the Super Bowl weekend. You can easily get 200 reservations and fill up your hotel. But, you are afraid that some people with reservations may not show up. The number of no-shows is Normally distributed with mean 5 and standard deviation 2. Room rate is $200/night. It costs hotel $300 to "bump" a customer. How many reservations should you take?