All trucks traveling on Interstate 40 between Albuquerqueand Amarillo are required to stop at a weigh station. Trucksarrive at the weigh station at a rate of 120 per eight-hourday (Poisson distributed), and the station can weigh, on theaverage, 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 theaverage waiting time before being weighed for each truck.b. If the truck drivers find out they must remain at theweigh station longer than 15 minutes on the average,they will start taking a different route or traveling atnight, thus depriving the state of taxes. The state ofNew Mexico estimates it loses $10,000 in taxes peryear for each extra minute (over 15) that trucks mustremain at the weigh station. A new set of scales wouldhave the same service capacity as the present set ofscales, and it is assumed that arriving trucks would lineup equally behind the two sets of scales. It would cost$50,000 per year to operate the new scales. Should thestate install the new set of scales?
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?
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