In a remote area of the jungle, there is a singleTL = 84 foot-long footbridge (across a deep canyon) that could only allow one person to cross at a time. The local volcano is due to erupt and the natives of the village must evacuate by crossing over the footbridge. During this evacuation, the natives arrive at this footbridge at a constant rate of l = 3 natives per minute and the speed v of a given native while walking across this footbridge is uniform between a = 3 feet per second and b = 7 feet per second. Of course, this means that the time for a native (walking with speed v) to cross the footbridge is T = Liv. a.) (3 points) Determine (in terms of L, a and b) the average time it takes for a given native to cross the footbridge. b.) (3 points) Determine the long-term average number of natives that will be waiting in line to cross the footbridge. c.) (3 points) Determine the long-term average time (in seconds) for a given native will be waiting in line to cross the footbridge. d.) (3 points) Determine the long-term average time (in seconds) for a given native will take to get out of the village. e.) (3 points) Determine the long-term average number of natives that will be getting out of the village. f.) (5 points) Verify your results in (a), (c) and (d) for using a simulation involving 10,000 natives (in order to get the long-term result)