Customers arrive at a barber shop at a rate of 6 /hr. Each customer gets a hairc

ID: 3276230 • Letter: C

Question

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 pro

fits,

show your work step by step:

a.Under the current model

b.If he leases 2 extra chairs at $ 20 per day per chair

c.If he keeps 4 chairs and hires a second barber (identical to him) for $30 /hr.

d.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 pi

What is the most profitable strategy?

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 one

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