Question

The wheat harvesting season in the American Midwest is​ short, and 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 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 and 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 ​$17 per hour. During the 2​-week harvest​ season, the storage bin is open and operated16 hours per​ day, 7 days per​ week, and can unload 34 trucks per hour according to a negative 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

​e) The total daily cost to the farmers of having their trucks tied up in the unloading process​ = ____ per day ​(round your response to the nearest whole​ number).

​f) As​ mentioned, the cooperative uses the storage bin heavily only 2 weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50​% next year. It will cost ​$8 comma ____ to do so during the​ off-season. The one-year net​ cost/benefit to enlarge the storage area​ =____ (round your response to the nearest whole​ number).

Answer 1