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A small manufacturing system produces parts for sea kayaks i…
A small manufacturing system produces parts for sea kayaks in La Jolla, San Diego. The parts arrive from an upstream Poisson process with an arrival rate of 1 part every 5 minutes. All the parts that enter the system must go through a station which houses 2 prefabrication machines. A part, though, only requires to be processed by 1 of the 2 machines during prefab. The prefab time is exponentially distributed with the same mean for each of 8 minutes. If all the machines at the prefab station are busy, then the part will wait for the next available machine. [HINT: The machines do NOT break down and thus do not need to be repaired]. a. What is the probability that both machines are idle? Please round your answer to 3 decimal places (e.g. #.###). [PartA] (4pts) b. What is the overall system utilization? [PartB] (2pts) c. What is the average number of parts waiting for prefab? [PartC] (2pts) d. A floor technician suggests that the system utilization rate should be lower (less than 30%) if the company wants to maintain the life of the machines and avoid machine failures. Do you think adding a third machine with the same processing rate will achieve that goal? Please show the new utilization rate to support your answer. Please express your answer to 3 decimal places and your asnwer (e.g., #.###, yes or #.###, no) and explain why on your scratch paper. [PartD] (2pts)
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