A manager of a hotel is considering how to restructure the front desk to reach an acceptable level of staff efficiency/utilization (at least 60%) and, at the same time, an average waiting time in the line/queue no longer than 10 minutes. At present, the hotel employs four clerks, each with a separate waiting line, during the peak check-in time. Observation of arrivals during this time shows that an average of 60 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 2.4 minutes for each front-desk clerk to register each guest. The manager is considering a number of plans for improving guest service by reducing the length of time guests spend waiting in line while keeping the utilization at least 60% Plan 1. Keep the current system as is, i.e., use four clerks, each with a separate waiting line Plan 2. Keep the four clerks, however, create only one, common, line in front of the four clerks Plan 3. Keep the current system as is, i.e., but employ only three clerks, each with a separate waiting line Plan 4. Use only three clerks and create only one, common, line in front of them The following additional cost information is available: - Customer waiting time in the line is valued at $5 per hour to reflect the fact that waiting time is annoying to the hotels clients. - The cost of employing each clerk is $25 per hour For each of the four plans above, calculate the following: a) the average number of clients waiting in the line b) the average number of clients in the system c) the average time a client waits in the line d) the average time a client waits in the system e) the utilization factor of the system f) the total cost (client waiting time + employee cost) of the plan.