5. Jobs arrive at a machine shop according to a Poisson distribution at the rate of 80...

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5. Jobs arrive at a machine shop according to a Poisson distribution at the rate of 80 jobs per week. An automatic machine represents the bottleneck in the shop. It is estimated that a unit increase in the production rate of the machine will cost $250 per week. Delayed jobs normally result in lost business, which is estimated to be $500 per job per week. Determine the optimum production rate for the automatic machine.

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