Consider the following Birth-Death process. In a barber shop, two barbers are working and on average...

 

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Consider the following Birth-Death process. In a barber shop, two barbers are working and on average it takes 45 minutes to do a hair cut, where these times are exponentially distributed. Potential customers arrive according to a Poisson process, with a rate of 2 potential customers per hour. When the potential customer sees no customers waiting, it surely enters the shop. If the potential customer sees k customers waiting, then the probability that he or she will enter the barber shop is 5-k. a. Model this as a continuous-time Markov chain. b. What is the probability that a potential customer will not enter the shop? 5 c. Suppose that a hair cut costs 25 and a barber costs 20 per hour. Should the owner of a barber shop hire a third barber, reduce the number of barbers to one or leave the situation as is? Consider the following Birth-Death process. In a barber shop, two barbers are working and on average it takes 45 minutes to do a hair cut, where these times are exponentially distributed. Potential customers arrive according to a Poisson process, with a rate of 2 potential customers per hour. When the potential customer sees no customers waiting, it surely enters the shop. If the potential customer sees k customers waiting, then the probability that he or she will enter the barber shop is 5-k. a. Model this as a continuous-time Markov chain. b. What is the probability that a potential customer will not enter the shop? 5 c. Suppose that a hair cut costs 25 and a barber costs 20 per hour. Should the owner of a barber shop hire a third barber, reduce the number of barbers to one or leave the situation as is?