John is planning on getting a haircut and wants to choose abarbershop. He narrowed his own choices down to 2 local hairsalons. Lets refer to them as hair salon 1 and hair salon 2.

During busy hours, a new customer walks into hair salon 1 every15 minutes with standard deviation of 15 minutes. At hair salon 2,a new customer walks in every 60 minutes with a standard deviationof 1 hour. Hair salon 1 has 4 barbers on staff, whereas hair salon2 has 1 barber. Service time at each hair salons is 30 minutes withstandard deviation of 30 minutes.

a) If John walks into hair salon 1 during a busy period, howlong must he wait in line before he can see a barber? (Note: onlycalculate the waiting time in the queue, not any service time).

b) If John walks into hair salon 2, how long must he wait inline before he sees a barber?

c) Assume that it takes John 10 minutes to leave home and walkto hair salon 1 and 10 minutes to walk back (i.e., 10 minutes eachway). Calculate how long he will be away from home if he gets hishaircut at hair salon 1?

d) Hair salon 1 is planning to buy out hair salon 2. Hair salon1 will then close the salon 2 operations and serve all customers,including existing hair salon 2 customers, at the salon 1 locationonly. Assuming that the previous traffic of salon 2 customers nowflows to the salon 1 location, what is the new averageinter-arrival time at salon 1 ?

e) To accommodate the new flow rate, hair salon 1 now staffs oneadditional barber (for a total of 5 barbers on staff). Is the newwaiting time at salon 1 less than or greater than the waiting timeof salon 1 before the merger? (Note: assume that the coefficient ofvariation of customer inter arrival times is 1).

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