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HW-10 Donna Shader, the manager of the Winter Park 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 3:00 P.M. to 5:00 P.M. Observation of arrivals during this time show that an average of 90 guests arrive each hour (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. Ms. Shader is considering a new plan. The new plan is to implement a single-line system. All guests could form a single waiting line to be served by whichever of five clerks became available. This option would require sufficient lobby space for what could be a substantial queue. For new plan, let Po = 0.005. The clerk is paid $25 per hour, but because of lost goodwill and sales, the Winter Park Hotel losses about $60 per hour of customer time spent waiting for the clerk to take an order. (Show all your work) 1. What is the average number of customers waiting to place a check-in service under the current system? 2. Determine the average amount of time that a guest spends checking in under the current system. 3. What is the total cost per hour under the current system? 4. What is the average number of customers waiting to place a check-in service under the new plan? 5. Determine the average amount of time that a guest spends checking in under the new plan. 6. What is the total cost per hour under the new layout? 7. Which option do you recommend and Why