Maths Solutions 26

Manning Auto operates an automotive service counter. While completing the repair work, Manning mechanics arrive at the company- parts department counter with an arrival rate of four per hour. The parts coordinator spends an average of 6 minutes with each mechanic, discussing the parts the mechanic needs and retrieving the parts from inventory.
a. Currently, Manning has one parts coordinator. On average, each mechanic wait is 4 minutes before the parts coordinator is available to answer questions or retrieve parts from inventory. Find𝐿𝐿𝑞𝑞, W, and L for this single-channel parts operation.
b. A trial period with a second parts coordinator showed that, on average, each mechanic waited only 1 minute before a parts coordinator is available. Find𝐿𝐿𝑞𝑞, W, and L for this two-channel parts operation.
c. If the cost of each mechanic is $20 per hour and the cost of each parts coordinator is $12 per hours, is the one-channel or the two-channel system more economical?

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