Problem 1 (25 pts): Suppose currently only I cookie maker is assigned to 6 machines that must be repaired whenever chocolate gets stuck in the gears. Suppose for each machine the running time between breakdown is known to be exponentially distributed with a mean running time of 4 hours. The service time required by a cookie maker to get the machine running is also exponentially distributed with the mean service time of 1 hour. 1) Draw the rate diagram for the problem. 2) What is the expected number of down machines and expected number of machines in queue? 3) What is the average number of cookie makers are busy? 4) What is the average waiting time in the system and in queue? 5) What is the server utilization? Problem 1 (25 pts): Suppose currently only I cookie maker is assigned to 6 machines that must be repaired whenever chocolate gets stuck in the gears. Suppose for each machine the running time between breakdown is known to be exponentially distributed with a mean running time of 4 hours. The service time required by a cookie maker to get the machine running is also exponentially distributed with the mean service time of 1 hour. 1) Draw the rate diagram for the problem. 2) What is the expected number of down machines and expected number of machines in queue? 3) What is the average number of cookie makers are busy? 4) What is the average waiting time in the system and in queue? 5) What is the server utilization