Question: A machine produces items one at a time, the production times being independent and identically distributed exponential random variables with mean 1 hour. The produced

A machine produces items one at a time, the production times being independent and
identically distributed exponential random variables with mean 1 hour. The produced
items are stored in a warehouse of capacity 5. When the warehouse is full the machine
is turned off, and it is turned on again when the warehouse has space for at least one
item. Demands for the items arrive according to a Poisson process with rate 20 per
day. Any demand that cannot be satisfied is lost.

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