Assignment:
Norfolk, Virginia, a major seaport on the East Coast, has a ship coal loading facility. Coal trucks filled with coal presently arrive at the port facility at mean rate of 149 per day (Poisson distributed). The facility operates 24 hours a day. The coal trucks are unloaded one at a time on a first-come, first-served basis by mechanical equipment that empties the trucks in a average time of eight minutes per truck regardless of truck size (exponentially distributed). The port authority is negotiating with a coal company for more trucks per day. However, the coal company will not use this port facility unless the port authority can assure them that its coal trucks will not have to wait to be unloaded at the port facility for more than 12 hours per truck on the average.
How many additional trucks should the port authority accept per day to meet the coal company's condition?
Provide complete and step by step solution for the question and show calculations and use formulas.