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  3. a small grocery store has a single checkout line.

A small grocery store has a single checkout line. On Saturdays, customers arrive at the checkout on...

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Advance Math

Asmall grocery store has a single checkout line. On Saturdays,customers arrive at the checkout on an average of one every 8minutes. The cashier takes an average of 6 minutes to process asingle customer. We assume that the service time is randomlydistributed, and the customers arrive randomly. The store's ownerbelieves that the amount of time that a customer has to wait hurtshis business; he estimates that waiting time costs him $20 percustomer-hour in lost business (i.e. Let's say 3 customers wait forone hour, the store incurs a cost of $20*3*1 = $60). In order tospeed up service, the owner is considering hiring a teenager to bagthe groceries at $6 per hour.
With the addition of the bagger, the cashier will be able toprocess a customer in an average of 4.5 minutes. Should the baggerbe hired?

Q1) Use queueing theory formulations to consult the storeowner. Show your work in terms of formulas utilized, computationsand discussion of results.

Q2) a brief discussion of your experimental results.

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