You operate a ferry service which carries tourists from Cape Cod to the island of Nantucket. You will charge customers $20 for each round trip reservation. You will refund 50% of the fare if the customer cancels more than 24 hours in advance. You pay fees per round trip for docking privileges of $3 in Cape Cod and $5 in Nantucket. You pay $150 in labor and fuel costs per round trip. Your ferry can accommodate 60 people. There will be three round trips per day. The likelihood of cancellations more than 24 hours in advance are displayed in the probability table below.

Number of Cancellations | Probability |

2 | .35 |

3 | .2 |

4 | .3 |

5 | .15 |

The demand for ferry trips follows a discrete uniform distribution between 45 and 65 customers. The likelihood of having no shows follow a discrete uniform distribution between 0 and 5 customers. You are willing to overbook your ferry service by 5 customers per round trip. If you donâ€™t have enough room to accommodate all of your customers, you pay a private charter service to carry the customers. The expected cost for the service (round trip per person) is normally distributed with a mean of $50 and a standard deviation of $5.

a) Simulate the profit per day. Replicate the calculations 200 time to determine the average profit per day.

b) Explore the profitability of an overbooking limit of 3, 4, and 5 customers per trip. Which do you recommend and why?