MonLab produces and sells computer monitors. Even though MonLab's monitors are quite reliable, some units fail soon after they are sold, in which case customers return them to retailers. Retailers send these monitors to MonLab's factory, where they are refurbished (repaired). Refurbished monitors are then sold at a lower price. Rabih is currently the only engineer at MonLab's factory responsible for repairing returned monitors. His job is quite simple. Returned monitors are delivered without any delay to his workstation. He takes one monitor at a time (in the order in which monitors arrive to his workstation), repairs it, and immediately sends it to the retailer. Having worked in electronics for over 20 years, Rabih can repair every monitor he receives. The repair time is on average half an hour and it is exponentially distributed. The factory receives on average 12 returned monitors per day and their arrival is a Poisson process. Assume that the above problem can be modeled by an M/M/S type-model. Write all necessary calculations. ( 1 day = 8hours) (5 points) What is the arrival rate of broken monitors and what is Rabih's service (repairing) rate? Express both rates as the number of monitors per hour. What is the utilization of the lab? (5 points) The manager of Rabih shows up unexpectedly in the middle of the shift. How many monitors he should expect to see waiting for repair? How many monitors on average Rabih is working on? (5 points) What is the rate per hour at which repaired monitors leave Rabih's workstation? (4 points) If a second engirieer was hired to repair change? Put x in the appropris (10 points) If a second engineer, Nadim, was hired to repair monitors. Two scenarios are considered. In the first scenario Rabih will receive on average half of the monitors and Nadim the other half. Each of them will have its own queue of monitors. In the second scenario all monitors arrive to one queue and each engineer work on whichever monitor is next in line. What is the utilization in each scenario? What is the average time a monitor waits for repair in each scenario? Is there a better scenario from a waiting time point of view? Explain carefully your calculations. Compare both scenarios. Conclude