Stefan Chirac has a cabana rental business in the exclusive resort of St. Tropez. Stefan can handle up to four cabanas daily. These must be assembled in the morning and taken down in the evening....

Stefan Chirac has a cabana rental business in the exclusive resort of St. Tropez. Stefan can handle up to four cabanas daily. These must be assembled in the morning and taken down in the evening. Stefan pays the company he gets the cabanas from a rental fee of $50 per cabana per day, and he rents the cabanas to tourists for either $80 or $100 per day.

 The weather in St. Tropez is either rainy, cloudy, or sunny. Each day there is a 10% chance of rainy weather, a 20% chance of cloudy weather, and a 70% chance of sunny weather. While Stefan must decide how many cabanas to rent before knowing what the weather will be, he can set the rental price after determining the day’s weather.

If the weather is rainy, there will be no rental demand. If the weather is cloudy, demand will follow a Poisson distribution with a mean of 2 if Stefan charges $80 for the rental and a mean of 1.5 if Stefan charges $100. If the weather is sunny, demand will follow a Poisson distribution with a mean of 4 if Stefan charges $80 and a mean of 3 if Stefan charges $100. Using a decision tree analysis, determine how many cabanas Stefan should rent and what price he should charge if the weather is cloudy or sunny.