In a massage shop, massagers requiring tools for massage present their request forms at the tools department counter. A tools clerk fills a request while the massagers wait. Massagers arrive at an average rate of 35 per hour -Poisson. A clerk can fill requests in 6 minutes -exponential. The tools clerks are paid $15 per hour and the massagers are paid $18 per hour.
- What is the optimal number of clerks? (you may start calculation from 4 clerks)
- The manager of the tools department decides to have 4 tools clerks. What is the probability that a new request will have to wait in line less than 3 minutes?