1. Queuing Theory. The Miller Manufacturing Company owns 500 identical machines that it uses in the production of colored nylon thread for the textile industry. Machine break downs occur following a Poisson distribution with an average of 0.004 break-downs occurring per operating hour per machine. The company employs two technicians working in a shop to fix these machines when they break down. Service times to repair the machines are exponentially distributed with an average of 0.3333333 hour per repair per technician (server). Answer " N/A " if answer is unavailable / unknown / cannot be calculated. Give a brief reason what your answer means or how you reach your answer. Show step(s) if applicable. Note that no definition asked. Do not answer a definition. 1.1 On average, number of machines that can be fixed in an hour is machine(s) 1.2 Minimum number of machine(s) in the shop at any time is(are) 1.3 On average, utilization of a technician is 1.4 The probability of both technicians are idle at the same time is 1.5 The probability of both technicians are fixing machines is 1.6 The average number of machine(s) in the shop is(are) machine(s) 1.7 The average number of machine(s) in the shop waiting in line is(are) machine(s) 1.8 The average time a machine spends waiting in line is hour(s) 1.9 The average time a machine spends in the shop is hour(s). 1.10 The minimum time a machine spends waiting in line is hour(s) 1.11 The maximum time a machine spends in the shop is hour(s) 1.12 The probability that there are twenty machines in the shop is