Question: Overbooking problem

The Arms Hotel in South Africa has only 56 rooms. An unfilled room represents R500 (rands) a night in lost profit, whereas every turn away due to a filled room costs R300 in ill will. If N reservations are accepted, the probability of N, N-1, and N-2 guests actually showing up is 0.2, 0.5, 0.3, respectively. How many reservations should be accepted?