The wheat harvesting season in the American Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively, and it is to every farmer’s benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays, the cost of truck rental, and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The storage bin is open and operated 16 hours per day, 7 days per week, during the harvest season and is capable of unloading 35 trucks per hour according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 30 per hour, following a Poisson pattern.
The cooperative, as mentioned, uses the storage bin only two weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off season.
1) The average number of trucks in the system is ____ trucks
2) The average time per truck spent in the system is____minutes
3) The utilization rate for the bin area is____ (Please round it to two decimal points.)
4) The probability that there are more than 3 trucks in the system is about____ (Please round it to two decimal points.)
5) The total daily cost in the unloading process is____per day (Please round it to two decimal points.)
6) Based on the above calculation, the net saving/loss of enlarging the bin is____dollars, hence the cooperative____proceed to enlarge the bin. (Please round to an integer and include no units. Use a "-" sign in front the number to indicate a net loss, if there is a loss. Also, enter only "should" or "should not" in the second blanket.)