Ty Webb, manager of the Philadelphia Hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At present, the hotel has five clerks on duty, each with a separate waiting line, during the peak check-in time of 3:00pm to 5:00pm. Observation of arrivals during this time shows that an average of 90 guests arrive each hour according to a Poisson process (although there is no upward limit on the number that could arrive at any given time). It takes an average of 3 minutes for the front-desk clerk to register each guest. The service times by the clerks are exponentially distributed.Mr. Webb is considering three plans for improving guest service by reducing the length of time guests spend waiting in line. The first proposal would designate one employee as a quick-service clerk for guests registering under corporate accounts, a market segment that fills about 30% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2 minutes on the average and also follows an exponential distribution. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 3.4 minutes. Under plan 1, noncorporate guests would choose any of the remaining four lines.The second plan is to implement a single-line system. All guests could form a single waiting line to be served by whichever of the five clerks became available. This option would require sufficient lobby space for what could be a substantial queue.The use of an automatic teller machine (ATM) for check-ins is the basis of the third proposal. This ATM would provide approximately the same service performance as would a clerk, however, the ATM’s service time would be a constant 3 minutes per guest. Given that initial use of this technology might be minimal, Webb estimated that 20% of customers, primarily frequent guests, would be willing to use the machines. This might be a conservative estimate if the guests perceive direct benefits from using the ATMs. Mr. Webb would set up a single queue for customers who prefer human interaction at check-in. This queue would be served by the five clerks, although Webb is hopeful that the machine will allow a reduction to four.Determine the average amount of time that a guest spends checking in. How would this change under each of the stated options? Which option would you recommend?