A computer repair shop, operated by a single technician, has room for at most two customers. Potential customers arrive at a Poisson rate of three per hour, and the successive service times are independent exponential random variables with mean 15 minutes. a) What is the average number of customers in the shop? Draw the rate diagram, clearly defining the states, and labeling all transition rates. b) What is the proportion of potential customers that leave the shop because it is too crowded?c) If the technician could work twice as fast, how much business would she do (e. g. what is the expected number of customers served per hour)? Draw the rate diagram, clearly defining the states and labeling all transitions ratesd) Now, if the technician was working at the original rate of 4 customers per hour, but she could hire an additional worker with the same service rate, how much business would the shop do (e. g. what is the expected number of customers served per hour)? Draw the rate diagram, clearly defining the states and labeling all transition rates.