a. (6 points) Suppose that you manage a hotel with 200 rooms in Richmond near the airport. There are generally two types of guests: (1) early guests who book rooms in advance; and (2) random guests who don't book the room until the last minute. Accordingly, you charge a bargain rate of $80 per night for the advance booking and a premium rate of $150 per night for the late booking. Based on previous observations, you are confident to fill all the 200 rooms with early guests as there are plenty of them. On the other hand, however, you are also interested in collecting the premiums from last-minute guests whose reservations follow a normal distribution with mean 75 and standard deviation 25. In order to maximize the hotel revenue per night, how many rooms are you going to reserve for the late booking? b. (6 points) On a given Vancouver-Toronto flight there are 200 seats. Suppose the ticket price is $475 on average and the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 6 and standard deviation 3. You decide to overbook the flight and estimate that the average loss from a passenger who will have to be "bumped" (if the number of passengers exceeds the number of seats) is $800. What is the maximum number of reservations that should be accepted