In an auto repair shop, mechanics requiring parts for auto repair present their request forms at the parts department counter. A parts clerk fills a request while the mechanics wait. Mechanics arrive at an average rate of $50$ per hour $($Poisson$).$ On average, a clerk can fill requests in $20$ per an hour $($exponential$).$ The cost of a parts clerk is $$30$ per hour and the waiting costs of a mechanic is $$60$ per hour. Because of the high arrival rate, an infinite source may be assumed. Determine the optimum number of clerks to staff the counter