A hotel near the university always fills up on the evening before football games. History has shown that when the hotel is fully booked, the number of last-minute cancellations has a mean of 7 and standard deviation of 5. The average room rate is $80. Assume that the variable cost for the room is $20. When the hotel is overbooked, the hotel has the following policy: they do not charge the customer the $80 and they provide the customer with a free room in the nearby high-end hotel. The hotel has to pay $180 for such a room. (A) What is the critical ratio for the number of rooms to overbook? (B) What is the optimal number of rooms to overbook?