1.(Critical path and capacity) Consider the following process flow diagram and accompanying table. This depicts a generic billing process flow, where resource pools work in parallel. That is, all splits in the flow are "AND". A job must flow through all resource pools in order to be completed. The average waiting time refers to the average wait in front of a resource pool. Assume that each resource pool has one server.(NOTE: This question does not use any queueing formulae.)a.[2] What is the cycle time of the billing process?(Hint: Cycle time includes both processing time and wait time.)b.[1] What is the capacity of the billing system in bills per|minute?(Hint: Capacity is based only on processing time.) Each of the three steps is performed by a dedicated worker (A, B, C) as indicated above. Work for a job is done in parallel along the top and bottom paths. A record kept of incoming jobs seems to indicate that the time between individual job arrivals is exponentially distributed with a mean of 12 minutes. Further, assume that the service times are exponentially distributed. What is the length of the critical path in minutes? (Hint: Each of the three steps is an M/M/1 queue.)3.[4] Consider the BIZEEBEE airline that has a reservations clerk taking calls. If the clerk is busy the caller is put on hold. The calls are taken in the order received. Assume that calls arrive exponentially \(\left(\mathrm{C}_{\mathrm{a}}{}^{2}=1 ight)\) at the rate of one every 6 minutes. The clerk takes on average 5 minutes to complete the reservation. The time for service is also assumed to be exponentially distributed (\(\mathrm{C}_{\mathrm{s}}^{2}=1\)). The clerk is paid \(\$ 20\) per hour. It has been estimated that each minute that a customer spends on hold costs BIZEEBEE \(\$ 2\) due to customer dissatisfaction and loss of future business. Estimate the average hourly cost.(Hint: First calculate wait time, \( C T_{q}\), using available queueing formulae and then use the available information to calculate average hourly cost. Note that both interarrival times and service times are exponentially distributed.)