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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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 per hour cost for customers waiting during repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La = L = W₁ = W = h h

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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 per hour cost for customers waiting during repair process. (a) What are the arrival rate and service rate in jobs per hour? (Round your answers to four decimal places.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La = L = W₁ = W = h h

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 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.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La L = Wa = = W = Wq 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 2.9 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 $31 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.) h h h h = 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 $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 $ Based on this, the director's argument should be ---Select--- ✓
Transcribed Image Text: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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 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.) λ = μ = (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La L = Wa = = W = Wq 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 2.9 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 $31 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.) h h h h = 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 $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 $ Based on this, the director's argument should be ---Select--- ✓
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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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 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.) λ = 0.25 μ = 0.3448 (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La 2.6902 L = 3.5241 X X Xh q W = 14.0965 Xh W = = 10.7632 Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $154.8676 X W (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 $31 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.) = q W = 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 $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 $ Based on this, the director's argument should be ---Select--- ✓
Transcribed Image Text: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 1.8 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $36 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.) λ = 0.25 μ = 0.3448 (b) Show the operating characteristics. (Round your answers to four decimal places. Report time in hours.) La 2.6902 L = 3.5241 X X Xh q W = 14.0965 Xh W = = 10.7632 Show the total cost per hour. (Express the total cost per hour in dollars. Round your answer to the nearest cent.) TC = $154.8676 X W (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 $31 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.) = q W = 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 $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 $ Based on this, the director's argument should be ---Select--- ✓
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