Problem 2 An average of 68 patrons/hr arrive at a hotel lobby (Poisson distribution), waiting to check in. At present, there are 5 clerks. Patrons wait 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/hour, and the hotel assesses a waiting time cost of $20 for each hour that a patron waits in line. Assume infinite queue and infinite population size. (A) What is the probability 5 patrons will arrive in a 15min period? (3 marks) (B) When a patron finally reaches the clerk, what is the probability it will take 20 seconds or more to check in? (3 marks) (C) One of the Clerks name is Bruce. What is the % of the time that Bruce is idle? (4 marks) (D) The hotel is considering replacing one of the clerk with an Automatic Clerk Machine (ACM). Management estimates of the 68 patrons/hr that arrive, 12 of them will use the ACM. Customers form a separate line at the ACM and assume that customers are not permitted to changes lines. An ACM takes an average of 1 min (exponential dist) to service each customer. It costs $8/day (1 day 8 hours) to operate an ACM. Should the hotel install the ACM? (10 marks)