Question $2(30$ pts$)$:

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$).$ Determine the following on worksheet Q$2$:

a$)$ If Newt walks into LHS during a busy period, how long must he wait in line?

b$)$ If Newt goes to SHC$,$ how many customers will he see at the salon?

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$?$

d$)$ LHS will buy out SHC$.$ LHS will then close SHC$\text{'}$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 and LHS now hires the barber from SHC $($to increase the headcount to $5).$ What is the new waiting time at LHS$?$ Is it less than or greater than the waiting time of LHS before the merger? Assume that the coefficient of variance of customer inter$-$arrival times, CVa $,$ is $1.$

You will need to set up the rest of the template. Please solve using excel and display formulas