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The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three 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 2.2 hours and a standard deviation of 1.4 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. (*) 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.) L- W- w 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 2.2 hours. For practical purposes, the standard deviation is o. Because of the computer-based system, the company's cost of the new operation would be $33 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.) W, W 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 $ 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 of there are no savings.) The average savings over a 40-hour work week amount to $ a Based on this, the director's argument should be Select A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 34 calls per hour. The service rate per line is 18 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Found your answers to four decimal places.) PCO) P(1) - P2) - A(3) - (D) What is the probability that an agent will be denied access to the system (Round your answers to four decimal places) (0) What is the average number of access lines in use?(round your answers to two decimal places) (d) in planning for the future, management wants to be able to handle d = 43 calls per hour. In addition, the probability that an agent will be denied access to the system should be no greater than the value computed in part (b). How many access lines should this system have? Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of three jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 2.2 hours and a standard deviation of 1.6 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs. (a) What is the mean arrival rate in jobs per hour? (Round your answer to four decimal places.) per hour (b) What is the mean service rate in jobs per hour? (Round your answer to four decimal places.) per hour (c) What is the average number of Jobs waiting for service? (Round your answer to four decimal places.) (d) What is the average time (in hours) a job waits before the welder can begin working on it? (Round your answer to two decimal places.) (e) What is the average number of hours between when a job is received and when it is completed? (Round your answer to two decimal places.) (1) What percentage of the time is Gubser's welder busy? (Round your answer to the nearest whole number.) % The Fore and Aft Marina is located on the Ohio River near Madison, Indiana, Fore and Aft currently operates a docking facility where only one boat at a time can stop for gas and servicing The manager of the Fore and Art Marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. Assume that the arrival rate is 3 boats per hour and that the service rate for each server is 8 boats per hour. (Round your answers to four decimal places. Report time in hours.) (a) What is the probability that the boat dock will be die? (b) What is the average number of boats that will be waiting for service? (c) What is the average time a boat will spend waiting for service? h (d) What is the average time a boat will spend at the dock? (e) If you were the manager of Fore and Aft Marina, would you be satisfied with the service level your system will be providing? Why or why not? Both channels will be empty approximately --Select- % of the time, and when customers do show up, they ---Select-- likely to have to wait for more than 5 minutes. On the whole, the expansion Select... be worth the needed investment