5. [5] Consider the following business process flow. Each order that arrives at the system is routed with a probability of 0.50 into one of the two branches as shown below. That is, the split is an "OR." Each step is performed by a single worker. The average processing rate of each of the 3 steps on the top is 6 jobs per minute. The average processing rate (in jobs per minute) of each of the 2 steps on the bottom is 5 jobs per minute. Assume a queue of orders of any length can be formed in front of each worker and the interarrival times of orders (at any station) as well as the processing times of each worker follow exponential distributions.

(a) [1] What is the capacity of the system, in orders per minute?

(b) [2] The marketing department requires that the average time in the system must be less than 2 minutes. Jeff, the business manager, accepted enough business that the throughput is 8 jobs per minute. Will Jeff satisfy the marketing department's requirement? Why or why not (please do report the average time that an order spends in the system, given Jeff's decision)?

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