Manning Autos operates an automotive service counter. While completing the repair work, Manning mechanics arrive at the company's 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 waits 4 minutes before the parts coordinator is available to answer questions or retrieve parts from inventory. Find Lq, 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 was available. Find Lq, 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 hour, is the one-channel or the two-channel system more economical?