the wheat harvesting season in the American Midwest is short, and a farmers deliver their truckloads of wheat to a giant central storage bin within a 2 week span. Because of this, wheat filled trucks waiting to unload and return to the fields have been known to back up for an entire block at the receiving bin. the cost of grain deterioration caused by unloading delays and the cost of truck rental and idle driver time are significant concerns to the farmers. the farmers estimate that the waiting and unloading cost for truck and driver is $19/hr. during the 2 week harvest season, the storage bin is open and operated 16 hours per day, 7 days a week, and can unload 34 trucks per hour according to an exponential distribution. full trucks arrive during the hours that the bin is open at a rate of about 31 per hour following a Poisson distribution.
a) what is the average number of trucks in the unloading system?
b) what is the average time per truck in the system?
c) what is the utilization rate for the bin area?
d) what is the probability that there are more than three trucks in the system at any given time?