2. (20 pts) Customers arrive at a barber shop at a rate of 6/hr. Each customer g
ID: 3302620 • Letter: 2
Question
2. (20 pts) Customers arrive at a barber shop at a rate of 6/hr. Each customer gets a haircut, which takes 15 minutes on average (assume service time is exponential). The barbershop has 4 barber's chairs, if a customer comes in and the barber is busy, they sit at an empty chair, and the barber eventually comes and gives them a haircut. If a customer comes to the shop and there are no chairs available, the customer leaves immediately. Assume that the barber's costs are on average $200 per day. He opens the shop 8 hours per day and charges 20 per haircut. Calculate the barber's daily profits, show your work step-by-step: a. b. c. d. Under the current model If he leases 2 extra chairs at $20 per day per chair If he keeps 4 chairs and hires a second barber (identical to him) for $30 /hr If he keeps 4 chairs and hires an apprentice that takes an average of 20min /haircut and costs $15/hr. Hint: For this part you can use MarkovExcel or Matlab to find What is the most profitable strategy?Explanation / Answer
a.T barber works 8 hours a day and serves 4 (15min per haircut ) customers per hour.
Total customers he serves in a day is 8*4 =32
total revenue he earns is 32*$20 = $640
Total profit = Revenue -cost =$640-$200 = $440
b. If 2 extra chairs are leased the Revenue remains the same as he can only service 4 customers in an hour but the cost goes up by $20 per chair
Hence profit goes down by $40 = $400
c. Now both the barbers together can service 8(working hours)*4(chairs)*2(barbers) = 64
but total customers that arrive at the shop are = 6*8= 48
hence the barbers can service only 48 customers
Total revenue = 48*20= $960
Total cost = $200(operational expense) + $30 = $230
total profit = $730
d.The new apprentice can service 3 customers per hour and 3*8=24 customers per day
Total customers they can service together in a day is 32+24 = 56
but the show can only accommodate 48 customers
Hence,total revenue = $960
Total cost = $200+$15 = $215
Total revenue = $745
Hence strategy in d part is the most profitable
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