An auto parts company is in the construction phase of a new plant in Lake Charles, LA. The centerpiece of the operation is a stamping machine that (in its basic configuration) can process 40 parts per hour (on average). Parts arrive at an average rate of 36 units per hour. Assume all processing (service) times and interarrival times are exponentially distributed. 9. Plant designers are trying to determine how large the waiting area in front of the press should be. How many parts should the waiting area be able to accommodate, on average? 10. The plant manager has a goal that (on average) no more than two parts will be in the waiting area at any given time. How much faster (service time in minutes) will the stamping machine have to perform in order to meet this goal? (Hint: to get an E[L] = 2 parts we can simply use the quadratic equation and solve for utilization, getting p= 0.72, before deriving our new value for u.) 11. Suppose the manager now has the option of purchasing a second machine (instead of trying to make the one machine faster as in the above problem). Under the current conditions (A= 36 and u= 40), will adding the second machine achieve the manager's goal of no more than two units (in either waiting area) if each machine takes on A/2 arrivals?