Question 3 (30 Points) A factory has 5 machine operators, who must request tools from a tool center when they need it. The tool requirement for each operator occurs according to a Poisson distribution at the rate of 2 per hour. Tool requests of operators are independent of each other. At present, the tool center is staffed by a clerk who is paid $6 per hour. The time it takes the clerk to handle each request follows exponential distribution with an average of 6 minutes. Since each operator produces $30 worth of goods per hour, each hour that an operator spends at the tool center costs the company $30. The company needs to decide whether it is worthwhile to hire a second clerk or not. If hired, the second clerk will be paid $4 per hour, and he will spend an exponentially distributed time to handle each request with an average of 10 minutes. (The second clerk will observe the first clerk if there is only one tool request). Should the second clerk be hired? Show all your calculations