### The average number of customers waiting for a haircut

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Benny the Barber owns a barber shop with two-chairs (stations for two barbers). However, he is the only barber working there at this time. His customers are arriving at the rate of one every thirty minutes. The arrival rate distribution follows a Poisson distribution as Benny does not take appointments. On average, it takes Benny an average of 24 minutes to give a haircut and this service time follows an exponential distribution. Using this information, answer the following questions.

a) The average number of customers waiting for a haircut.

b) The average time a customer is in the shop.

c) Suppose Benny’s waiting area has only three chairs for waiting customers. What percent of the time will a customer arriving not be able to find a chair to sit in?

d) Benny is concerned about losing revenue and is considering adding another barber. He believes that for every hour a customer is in his shop either waiting for a haircut or having his haircut he loses \$3 of revenue. If he hires the barber, he will pay him a salary of \$10 per hour. Benny currently pays himself \$15 for cutting hair. Answer the following questions for the two-chair operation. Assume that the arrival rate will not change and that the second barber will work at the same pace as Benny. Customers cannot ask for a specific barber but will take the first one available.

Based on the cost of the operation and using the information provided here, which operation (Benny or Benny combined with the second barber) would be the most cost effective? Provide the cost of operation of each scenario. Base your cost analysis only on the information provided here and ignore the time value of money.

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