Costco customer service has two service desks, one at each entrance of the store
ID: 437883 • Letter: C
Question
Costco customer service has two service desks, one at each entrance of the store and management considers them as separate entitites. Customers arrive at the front entrance desk at an average of one every six minutes, while at the back entrance desk they arrive at an average of one every three minutes. The service rate at each service desk is four minutes per customer.1. How often (% of time) is each service desk busy?
2. How many customers, on average, are waiting in line at each desk?
3. How much time does a customer spend at each service desk (waiting time plus service time)?
Explanation / Answer
Costco customer service has two service desks, one at each entrance of the store and management considers them as separate entities. Customers arrive at the front entrance desk at an average of one every six minutes, while at the back entrance desk they arrive at an average of one every three minutes.
The service rate at each service desk is four minutes per customer.
1.How often (% of time) is each service desk busy?
Front: One customer every six minutes, and it takes 4 minutes per customer = 4 out of every six minutes are busy = the desk is busy 2/3rd of the time = 66.67%
Back: Since it takes 4 min. to service a customer but one comes in every 3 minutes, this desk is busy 100% of the time.
2.How many customers, on average, are waiting in line at each desk?
Front: zero, since there's enough time to service each incomer.
Back: One customer every three min vs. four min to service a customer = 1 customer "accumulates"
Hence there's an average of one customer in line for the back desk.
3.How much time does a customer spend at each service desk (waiting time plus service time)?
Front: Just 4 minutes, since he's automatically serviced!
Back: Since there's an average of one customer, the newcomer has to wait for both the person in front of him and for himself to be serviced; so, 3 min of waiting + 4 min of own servicing = 7 minutes
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