Question 25 (10 points) David is planning on getting a haircut and wants to choose a barbershop. He narrowed his choices down to two local hair salons. Lets refer to them as hair salon 1 and hair salon 2. During busy hours, a new customer walks into 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. Answer the following questions based on the information provided. Provide your detailed answers in the text box, explain how you arrived at your answers and which formula you used. a) If David walks into hair salon 1 during a busy period, how long must he wait in line before he can see a barber? (Note: only calculate the waiting time in the queue, not any service time). (2 marks) b) If David walks into hair salon 2, how long must he wait in line before he sees a barber ? (2 marks) c) Assume that it takes David 10 minutes to leave home and walk to hair salon 1 and 10 minutes to walk back (i.e., 10 minutes each way). Calculate how long he will be away from home if he gets his haircut at hair salon 1 ? d) 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 ? (2 marks) e) 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 ? (2 marks) (Note: assume that the coefficient of variation of customer inter-arrival times is 1)