Three prospective designs are under consideration for a manufacturing cell. The first uses $3$ parallel machines each with service rate $,$ a common queue, and total arrival rate $.$ The second option uses the same machines but has a separate queue for each machine. Arriving part batches will be randomly assigned to a machine. The third configuration consists of one fast machine, which serves at the rate of $3.$ Ignoring the capital and operating costs, which system has the lowest throughput time and WIP levels? You may assume inter$-$arrival and service times are exponential and let $=5$ and $=10.$