Questior The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service one customer every six minutes. Cars arrive at the regular unleaded pump at an average of 6 customers per hour. a) What is the average time a customer waits in the queue to receive service? b) Management of Petroco likes to have its operators working 90% of the time. What must the arrival rate be for the pump attendant to be as busy as management would like? c) The average waiting time computed in (a) above is not pleasant to management and it wishes to reduce it. There are two alternatives open to management. First, management can add an assistant to the attendant and this will improve the service rate to one customer every four minutes. This assistant will receive a salary of GHC100 per month. The second alternative is that management can add a second pump which will cost GHC2,000 and this amount is a free gift from Suobogbiree & Sons. This alternative will reduce the arrival rate to 3 every hour however, Petroco will have to pay the attendant a monthly salary of GHC150. Whichever alternative management adopts, Petroco avoids a lost sale of GH¢100 for every minute that average waiting time is reduced. Could you advise management which alternative it must adopt?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Questior
The Petroco Service Station has one pump for regular unleaded gas, which
(with an attendant) can service one customer every six minutes. Cars arrive at
the regular unleaded pump at an average of 6 customers per hour.
a) What is the average time a customer waits in the queue to receive
service?
b) Management of Petroco likes to have its operators working 90% of
the time. What must the arrival rate be for the pump attendant to be
as busy as management would like?
c) The average waiting time computed in (a) above is not pleasant to
management and it wishes to reduce it. There are two alternatives
open to management. First, management can add an assistant to the
attendant and this will improve the service rate to one customer
every four minutes. This assistant will receive a salary of GH¢100 per
month. The second alternative is that management can add a second
pump which will cost GH¢2,000 and this amount is a free gift from
Suobogbiree & Sons. This alternative will reduce the arrival rate to 3
every hour however, Petroco will have to pay the attendant a monthly
salary of GH¢150. Whichever alternative management adopts,
Petroco avoids a lost sale of GH¢100 for every minute that average
waiting time is reduced. Could you advise management which
alternative it must adopt?
Transcribed Image Text:Questior The Petroco Service Station has one pump for regular unleaded gas, which (with an attendant) can service one customer every six minutes. Cars arrive at the regular unleaded pump at an average of 6 customers per hour. a) What is the average time a customer waits in the queue to receive service? b) Management of Petroco likes to have its operators working 90% of the time. What must the arrival rate be for the pump attendant to be as busy as management would like? c) The average waiting time computed in (a) above is not pleasant to management and it wishes to reduce it. There are two alternatives open to management. First, management can add an assistant to the attendant and this will improve the service rate to one customer every four minutes. This assistant will receive a salary of GH¢100 per month. The second alternative is that management can add a second pump which will cost GH¢2,000 and this amount is a free gift from Suobogbiree & Sons. This alternative will reduce the arrival rate to 3 every hour however, Petroco will have to pay the attendant a monthly salary of GH¢150. Whichever alternative management adopts, Petroco avoids a lost sale of GH¢100 for every minute that average waiting time is reduced. Could you advise management which alternative it must adopt?
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