All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 120 per eight-hour day (Poisson distributed), and the station can weigh, on the average, 140 trucks per day (Poisson distributed).
a. Determine the average number of trucks waiting, the average time spent at the weigh station by each truck, and the average waiting time before being weighed for each truck.
b. If the truck drivers find out they must remain at the weigh station longer than 15 minutes on the average, they will start taking a different route or traveling at night, thus depriving the state of taxes. The state of New Mexico estimates it loses $10,000 in taxes per year for each extra minute (over 15) that trucks must remain at the weigh station. A new set of scales would have the same service capacity as the present set of scales, and it is assumed that arriving trucks would line up equally behind the two sets of scales. It would cost $50,000 per year to operate the new scales. Should the state install the new set of scales?