A barbershop has two barbers: an experienced owner and an apprentice. The owner cuts hair at the rate of 4 customers/hour, while the apprentice can only do 2 cus- tomers/hour. The owner and the apprentice work simultaneously, however any new customer will always go first to the owner, if the latter is available. The barbershop has waiting room for only 1 customer (in case both barbers are busy), any additional customers are turned away. Suppose customers walk by the barbershop at the rate of 6 customers/hour. (a) Construct a continuous-time Markov chain for this problem and explain your assumptions. (b) Write down the infinitesimal generator G of this chain. (c) Using your model find the proportion of time the apprentice is busy cutting hair.