The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the...

  

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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 2.9 hours and a standard deviation of 2.1 hours. The company's cost of the repair operation is $27 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.) À = 2500 - 3448 (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La W = Wa h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ Xh (c) The company is considering purchasing a computer-based equipment repair system that would enable a constant repair time of 2.9 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 $30 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 = xh Xh Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ x (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 $3 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 $ should be contested x . Based on this, the director's argument 5. [0/20 Points] DETAILS PREVIOUS ANSWERS CAMMIMS16 11.E.030. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 29 calls per hour. The service rate per line is 19 calls per hour. x x x x (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = 3071 P(1) - 3570 P(2) = 2074 P(3) 0954 (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P=0954 x (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 1.53 x (d) In planning for the future, management wants to be able to handle λ = 40 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? 0954 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 2.9 hours and a standard deviation of 2.1 hours. The company's cost of the repair operation is $27 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.) À = 2500 - 3448 (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La W = Wa h Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ Xh (c) The company is considering purchasing a computer-based equipment repair system that would enable a constant repair time of 2.9 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 $30 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 = xh Xh Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $ x (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 $3 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 $ should be contested x . Based on this, the director's argument 5. [0/20 Points] DETAILS PREVIOUS ANSWERS CAMMIMS16 11.E.030. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 29 calls per hour. The service rate per line is 19 calls per hour. x x x x (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = 3071 P(1) - 3570 P(2) = 2074 P(3) 0954 (b) What is the probability that an agent will be denied access to the system? (Round your answers to four decimal places.) P=0954 x (c) What is the average number of access lines in use? (Round your answers to two decimal places.) 1.53 x (d) In planning for the future, management wants to be able to handle λ = 40 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? 0954