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Problem 11-17 (Algorithmic) The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aft decides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow a Poisson probability distribution, with an arrival rate of 15 boats per hour, and that service times follow an exponential probability distribution, with a service rate of 20 boats per hour. The manager of the Fore and Aft Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Note: Use Po values from Table 11.4 to answer the questions below. a. What is the probability that the boat dock will be idle? Round your answer to four decimal places. 3 X b. What is the average number of boats that will be waiting for service? Round your answer to four decimal places. La 3 c. What is the average time a boat will spend waiting for service? Round your answer to four decimal places. Wq = 0.15 x hours d. What is the average time a boat will spend at the dock? Round your answer to four decimal places. W = 0.2 X hours e. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing? Yes Why or why not? Round your answers to whole numbers. Because the average wait time is 3 X seconds. Each channel is idle 25 X % of the time. Feedback Check My Work Partially correct Solution: Given that, X= - 15/hour = = 20/hour k=1 Hence, a: Probability of no boats in the system. 1 1 15 20 0.25 = 25% Al b: Average number of boats waiting for service: 2 L= 15 = 3 boats 20 15 Il- 15 La = 2 3 2.25 boats 20 c: Average time boat spends waiting for service: La 2.25 WA 0.15 hours 15 d: Average time spent in the system: L W 3 15 0.2 hours **I am bounded by Chegg policy to solve only the first four question parts**