A restaurant prepares Peking duck daily at a cost of $18 per duck. Each duck generates revenue of $47 if sold. Demand for Peking duck can be described by a Poisson distribution with a mean of 4.2 ducks per day. Unsold ducks at the end of each day are converted to duck soup at an additional cost of $5 over and above the resulting value as soup. How many ducks should be prepared each day?