In the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 60 per hour, and a clerk can fill requests at the rate of 30 per hour (exponential). If the cost for a parts clerk is $30 per hour and the cost for a mechanic is $60 per hour, answer the following three questions (Because of the high arrival rate, an infinite source may be assumed.)
At least how many clerks to staff the counter?
How many mechanics are waiting in line on average?
What is the optimum number of clerks to staff the counter?