The Winter Park Hotel manager, Donna Shader, is considering restructuring the front desk to reach optimum staff efficiency and guest service level. At present, the hotel has three clerks on duty, each with a separate waiting line, during the peak check-in time of 3:00 PM to 5:00 PM Observation of inter- arrival time during this time show that an average inter-arrival time is 2 minute (although there is no upward limit on the number that could arrive at any given time). An average of 12 customers can be served per hour for the front desk clerk to register each guest. Assuming that inter-arrival times and service times are exponential. Ms. Shader is considering a new plan for improving quest service by reducing the length of time the quest spends waiting in line. The new plan is to implement a single-line system. All guests could form a single waiting line to be served by whichever three clerks became available. This option would require sufficient lobby space for what could be a substantial queue. Discussion Questions (Calculate down to three decimal points) Problem 1: Determine P, and the average amount of time (W: Minutes) that a guest spends checking in. (a: 6 points, b: 14 points) a) Current Plan: Po W b) New Plan: Po = W= Problem 2: What is your recommendation? Why? (5 points)