A family-operated inn in State College, Pennsylvania, is considering overbooking to minimize their..

A family-operated inn in State College, Pennsylvania, is
considering overbooking to minimize their revenue loss due to no-shows and
last-minute cancellations. The cost of an empty room is estimated at $95 per
night. When the inn is fully occupied, customers with guaranteed reservations
are placed in nearby expensive hotel chains, averaging $165 per night. In
addition to paying the difference in room rates, the inn also gives a $20
voucher for taxi fare. Determine the inn’s overbooking policy, given that the
distribution of no-shows is Uniform over the interval (5, 25).