Q2. An average of 24 customers/hr arrive at a small Driver Licensing Office (Poisson distribution) waiting to renew their driver's license, update their vehicle registration sticker, etc. At present, there are 3 clerks. Customers wait in a single line for the first available clerk. The average time for a clerk to service a customer is 4min (exponentially dist). Clerks earn $12/hr and the government assesses a waiting time cost of $20 for each hour that a customer waits in line. (a) When a customer finally reaches the clerk, what is the probability it will take 25 seconds or more to complete service? (b) What is the expected cost per hour to operate the office? (c) What is the probability you will not have to wait in line when you come to this office? (d) The government is considering replacing one of the clerk with an Automatic Service Machine (ASM). Management estimates of the 24 customers/hr that arrive, 20% of them will use the ASM. Customers form a separate line at the ASM and assume that customers are not permitted to changes lines. An ASM takes an average of 8 min (exponential dist) to service each customer. It costs $5/hr to operate the ASM. Should the government install the ASM? Q2. An average of 24 customers/hr arrive at a small Driver Licensing Office (Poisson distribution) waiting to renew their driver's license, update their vehicle registration sticker, etc. At present, there are 3 clerks. Customers wait in a single line for the first available clerk. The average time for a clerk to service a customer is 4min (exponentially dist). Clerks earn $12/hr and the government assesses a waiting time cost of $20 for each hour that a customer waits in line. (a) When a customer finally reaches the clerk, what is the probability it will take 25 seconds or more to complete service? (b) What is the expected cost per hour to operate the office? (c) What is the probability you will not have to wait in line when you come to this office? (d) The government is considering replacing one of the clerk with an Automatic Service Machine (ASM). Management estimates of the 24 customers/hr that arrive, 20% of them will use the ASM. Customers form a separate line at the ASM and assume that customers are not permitted to changes lines. An ASM takes an average of 8 min (exponential dist) to service each customer. It costs $5/hr to operate the ASM. Should the government install the ASM