An average of 40 jobs per day arrive at a factory. Thetime between arrivals of jobs is exponentially distributed.The factory can process an average of 42 jobs per day, andthe time to process a job is exponentially distributed.a What is the probability that exactly 180 jobs arriveat the factory during a 5-day period?b On the average, how long does it take before a jobis completed (measured from the time the job arrives atthe factory)?c What fraction of the time is the factory idle? d What is the probability that work on a job will be-gin within 2 days of its arrival at the factory?
An average of 40 jobs per day arrive at a factory. Thetime between arrivals of jobs is exponentially distributed.The factory can process an average of 42 jobs per day, andthe time to process a job is exponentially distributed.a What is the probability that exactly 180 jobs arriveat the factory during a 5-day period?b On the average, how long does it take before a jobis completed (measured from the time the job arrives atthe factory)?c What fraction of the time is the factory idle? d What is the probability that work on a job will be-gin within 2 days of its arrival at the factory?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
An average of 40 jobs per day arrive at a factory. The
time between arrivals of jobs is exponentially distributed.
The factory can process an average of 42 jobs per day, and
the time to process a job is exponentially distributed.
a What is the probability that exactly 180 jobs arrive
at the factory during a 5-day period?
b On the average, how long does it take before a job
is completed (measured from the time the job arrives at
the factory)?
c What fraction of the time is the factory idle?
d What is the probability that work on a job will be-
gin within 2 days of its arrival at the factory?
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