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A Post Office Has a Single Line for Customers Waiting

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A post office has a single line for customers waiting for the next available postal clerk.There are two postal clerks who work at the same rate.The arrival rate of customers follows a Poisson distribution,while the service time follows an exponential distribution.The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks.What proportion of time are both clerks idle?

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Definitions:

Economizing Problem

The need to make choices about how to best use limited resources to satisfy unlimited wants.

Limited Resources

The economic principle that the available resources (such as time, money, and raw materials) are insufficient to satisfy all wants and needs.

Unlimited Wants

The economic concept that human desires and needs are infinite and vary in intensity, contrasting with limited available resources.

Normative

In economics and philosophy, refers to statements or propositions that express values, ethics, or moral prescriptions, indicating how things ought to be.

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