In a machine shop, the failure rate of machines follows Poisson Distribution with a mean rate of

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In a machine shop, the failure rate of machines follows Poisson Distribution with a mean rate of failure of 7 machines per day. The maintenance time of the breakdown machines follows negative exponential distribution with a mean service time of 6 minutes by a single mechanic.

The cost of downtime of a machine is ! 4000 per hour. The wage of the maintenance mechanic is ! 150 per day. Find the optimal number of mechanics to be assigned for maintenance work such that the sum of the cost of downtime of the machines and the cost of mechanics is minimized. Assume eight hours per shift and one shift per day.

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