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Problem A room has 10 cotton spinning looms. Once the looms are set up, they run automatically. The setup time is exponentially distributed, with mean 10 minutes. The machines run for an average of 40 minutes, also exponentially distributed. Loom operators are paid $10 an hour, and looms not running incur a cost of $40 an hour.
1. How many loom operators should be employed to minimize the total cost of the loom room?
2. How many people should be employed so that no loom waits more than 1 minute for an operator?
3. How many operators should be employed to ensure that, on average, at least 7.5 looms are running at all times?
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