The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of two jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 3.0 hours and a standard deviation of 1.9 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $37 per hour cost for customers waiting during the repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) ?=?= (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) Lq=L=Wq= hW= h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $  (c) The company is considering purchasing a computer-based equipment repair system that would enable a constant repair time of 3.0 hours. For practical purposes, the standard deviation is 0. Because of the computer-based system, the company's cost of the new operation would be $32 per hour. What effect will the new system have on the waiting line characteristics of the repair service? (Round your answers to four decimal places. Report time in hours.) Wq= hW= h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $  (d) Does paying for the computer-based system to reduce the variation in service time make economic sense? The firm's director of operations rejected the request for the new system because the hourly cost is $4 higher and the mean repair time is the same. Do you agree? How much (in dollars) will the new system save the company during a 40-hour work week? (Round your answer to the nearest cent. Enter 0 if there are no savings.) The average savings over a 40-hour work week amount to $  . Based on this, the director's argument should be

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is five trucks per hour. Use the Single Server Queue Excel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?   truck(s) What is the average number of trucks in the system?   truck(s) What is the average time a truck spends in the queue waiting for service?   hour(s) What is the average time a truck spends in the system?   hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places.   What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?  truck(s) What is the average number of trucks in the system?  truck(s) What is the average time a truck spends in the queue waiting for service?  hour(s) What is the average time a truck spends in the system?  hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane?(h) A cash machine manufacturer has offered an advanced system that willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.