Reference no: EM131619363

Question: At a small rock quarry, a single power shovel dumps a scoop full of rocks at the loading area approxi-mately every 10 minutes, with the actual time between scoops modeled well as being exponentially distributed, with mean 10 minutes. Three scoops of rocks make a pile; whenever one pile of rocks is completed, the shovel starts a new pile. The quarry has a single tuck that can carry one pile (3 scoops) at a time. It takes approximately 27 minutes for a pile of rocks to be loaded into the truck and for the truck to be driven to the processing plant, unloaded, and return to the loading area. The actual time to do these things (altogether) is modeled well as being normally distributed, with mean 27 minutes and standard deviation 12 minutes. When the truck returns to the loading area, it will load and transport another pile if one is waiting to be loaded; otherwise, it stays idle until another pile is ready. For safety reasons, no loading of the truck occurs until a complete pile (all three scoops) is waiting. The quarry operates in this manner for an 8-hour day. We are interested in estimating the utilization of the trucks and the expected number of piles waiting to be transported if an additional truck is purchased.