please answer all The new Fore and Aft Marina is to be located on the Ohio River near Madison, Indiana. Assume that Fore and Aftdecides to build a docking facility where one boat at a time can stop for gas and servicing. Assume that arrivals follow aPoisson probability distribution, with an arrival rate of 8 boats per hour, and that service times follow an exponentialprobability distribution, with a service rate of 10 boats per hour. The manager of the Fore and Aft Marina wants toinvestigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicingsimultaneously.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.Po =b. What is the average number of boats that will be waiting for service? Round your answer to four decimal places.System A$System BSSystem C$System (La =|c. What is the average time a boat will spend waiting for service? Round your answer to four decimal places.Wq =d. What is the average time a boat will spend at the dock? Round your answer to four decimal places.W =hoursA fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 12 cars per hour, and thatservice times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive theirorders. The following three service alternatives are being considered:System A: A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2.5 minutes.System B: A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 2 minutes.System C: A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money for customers arriving at the window. The averageservice time for this alternative is 2.5 minutes for each server.hourse. If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will beproviding?The following cost information is available.• Customer waiting time is valued at $25 per hour to reflect the fact that waiting time is costly to the fast-food business.• The cost of each employee is $9.5 per hour.• To account for equipment and space, an additional cost of $20 per hour is attributable to each server.What is the lowest-cost design for the fast-food business? Round your answers to the nearest cent.Note: Use Po values from Table 11.4 to answer the questions below.Total Cost/houris the most economical.PreviousNex Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to aPoisson probability distribution, with an arrival rate of 15 customers per hour. The checkout service times follow an exponential probabilitydistribution, with a service rate of 25 customers per hour. The manager's service goal is to limit the waiting time prior to beginning thecheckout process to no more than five minutes. Also the manager of Pete's Market wants to consider one of the following alternatives forimproving service. Calculate the value of Wq for each alternative.a. Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from thecustomer. With this improved single-server operation, the service rate could be increased to 32 customers per hour. Round your answer tothree decimal places. Do not round intermediate calculations.Wq =b. Hire a second person to operate a second checkout counter. The two-server operation would have a service rate of 25 customers per hourfor each server. Note: Use Po values from Table 11.4 to answer this question. Round your answer to three decimal places. Do not roundintermediate calculations.Wq =minutesRecommendWhat alternative would you recommend? Justify your recommendation.minutesThe two counone checkout counter with two employeestwo checkout counters with two employeesWhat alternative would yRecommendThe two counter systemhas better service but costs morehas better service and is cheaperhas worse service but is cheaperhas worse service and costs morehmendation.

Question

Accepted Answer

Find the Calculation methods below:
Single server:

Multiple servers:

Total cost:
Total cost = Cw*L…