2. (30 points) all trucks traveling on interstate 40 between albuquerque and amarillo are required to stop at a weight station. trucks arrive at the weight station at a rate of 90 per eight-hour day (poisson distributed), and the station can weight, on the average, 110 trucks per eight-hour day (poisson distributed). a. determine (i) the average number of trucks waiting, (ii) the average time spent at the weight station by each truck, (iii) the average waiting time before being weighted for each truck. b. if the truck drivers find out they must remain at the weight station longer than 15 minutes on the average, they will start taking a different route or travelling at night, thus depriving the state of taxes. the state of new mexico estimates it loses $8,000 in taxes per year for each extra minute (over 15 minutes) that trucks must remain at the weight station. a new set of scales would have the same capacity as the present set of scales and it is assumed that arriving trucks would line up equally behind the two set of scales. it would cost $60,000 per year to operate the new scales. should the state install the new set of scales? why? show your work.