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John is planning on getting a haircut and wants to choose a barbershop. He narrowed his own choices down to 2 local hair salons. Lets refer to them as hair salon 1 and hair salon 2.
During busy hours, a new customer walks into hair salon 1 every 15 minutes with standard deviation of 15 minutes. At hair salon 2, a new customer walks in every 60 minutes with a standard deviation of 1 hour. Hair salon 1 has 4 barbers on staff, whereas hair salon 2 has 1 barber. Service time at each hair salons is 30 minutes with standard deviation of 30 minutes.
a) Hair salon 1 is planning to buy out hair salon 2. Hair salon 1 will then close the salon 2 operations and serve all customers, including existing hair salon 2 customers, at the salon 1 location only. Assuming that the previous traffic of salon 2 customers now flows to the salon 1 location, what is the new average inter-arrival time at salon 1 ?
b) To accommodate the new flow rate, hair salon 1 now staffs one additional barber (for a total of 5 barbers on staff). Is the new waiting time at salon 1 less than or greater than the waiting time of salon 1 before the merger? (Note: assume that the coefficient of variation of customer inter arrival times is 1).
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