A marina operates with two machines that put boats into the water. Each machine has a stuarall line. Boat owners arrive according to a Poison process. After the boat owners arrive, they rall domly choose one of the two lines to join, with the probability of choosing a particular line equal to the probability of choosing the other line. . Once a boat owner enters a line, It is not possible for the boat owner to maneuver his/her way into the other line. Each machine operates as follows. Boat owners reverse their trailers into the machine - which operates like a large sling and lowers the boat intO the water. The time to serve a customer at 100%. chine follows an exponential distribution. Historical data show that it takes, on average, 50 minutes from the arrival of a boat owner till the time his/her boat is put into water. The average waiting time in line is 40 minutes. on average, there are 4 boats in the system for each machine, including those waiting in line and those being served by the machine

1. (10 points) What is the average service rate of each machine? Give your answer in number of boats per hour. Note that this number does not need to be an integer number.

2. (10 points) What is the average rate of customer arrival to the marina? Give your answer in number of customers per hour. Note that this number does not need to be an integer number.

3. What is the probability that a customer can be served immediatly upon their arrival, without waiting?

4. What is the utilization of the machines?

5. The manager of the marina feels that the average waiting time in line is too long. He feels that customers may switch to a cpmpetitor and he may, thus lose business. He has decided to change the system into one that has a single line serving both machines in the marina. The arrival process of customers remains unaffected and the time to serve a customer at a machine is also unchanged. In this new system, what is the average waiting time for a boat owner before his/her boat enters service of a machine?

6. Calculate the difference, if any in the average number of customers waiting in line in the old and new systems. Explain the difference if any.