To help fill its seats for a particular flight, an airline offers a special nonrefundable fare of $100 for customers who make a reservation at least 21 days in advance and satisfy other restrictions. Thereafter, the fare will be $300. A total of 100 reservations will be accepted. The number of customers who have requested a reservation at full fare for this flight in the past always has been at least 31 and not more than 50. It is estimated that the integer numbers between 31 and 50 are equally likely.
Use the model for capacity-controlled discount fares to determine how many of the reservations should be reserved for customers who would pay full fare.