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John Smith needs to decide where to get a haircut. He decides to pick one based on how much time he has to take off from work. He has narrowed the choice down to two local hair salons - Large Hair Salon (LHS) and Small Hair Cutters (SHC). During busy periods, a new customer walks into LHS every 15 minutes (with a standard deviation of 15 minutes). At SHC, a customer walks in every hour (with a standard deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. A typical service time at either salon lasts 30 minutes (with a standard deviation of 30 minutes).
(a) If John's office is at a 10-minute walking distance from both hair salons, how much time (on average) does John need to take off from work to get a hair-cut and get back to work?
(b) Consider the scenario where LHS buys out SHC, closes SHC's operations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location (with the same coefficient of variation), and that SHC's personnel also joins LHS what is new average wait time?
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