Problem:
Newt Philly needs to decide where to get a haircut. 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).
Required:
Question a) If Newt walks into LHS during a busy period, how long must he wait in line before he can see a barber?
Question b) If Newt goes to SHC, how long must he wait in line before his haircut starts?
Question c) Assume that it takes Newt 10 minutes to leave work and walk to LHS and 10 minutes to walk back (i.e. each way of the walk takes 10 minutes). How long will he need to leave work for to get a haircut at LHS?
Question d) LHS will buy out SHC. LHS will then close 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, what is the new inter-arrival time at LHS?
Question e) To accommodate the new flow rate, LHS now staffs one additional barber (to increase the headcount to 5). Is the new waiting time at LHS less than or greater than the waiting time of LHS before the merger? (Assume that the coefficient of variation of customer inter-arrival times is 1).
Provide thorough explanation of the given question.