An average of 90 patrons per hour arrive at a hotel lobby (interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a single line for the...

An average of 90 patrons per hour arrive at a hotel lobby (interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a single line for the first available clerk. The average time for a clerk to service a patron is 3 minutes (exponentially distributed). Clerks earn $10 per hour, and the hotel assesses a waiting time cost of $20 for each hour that a patron waits in line.

a Compute the expected cost per hour of the current system.

b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management estimates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron. It costs $48 per day (1 day = 8 hours) to operate an ACM. Should the hotel install the ACM? Assume that all customers who are willing to use the ACM wait in a single queue.