Business, 01.11.2021 01:00 Rakeem458

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 -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 $ per hour. During the -week harvest season, the storage bin is open and operated hours per day, 7 days per week, and can unload 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 per hour, following a Poisson pattern. To help the cooperative get a handle on the problem of lost time while trucks are waiting in line or unloading at the bin, find the following:

a) The average number of trucks in the unloading system =
5 trucks (round your response to two decimal places).

b) The average time per truck in the system =
10 minutes (round your response to the nearest whole number).

c) The utilization rate for the bin area =
. 833 (round your response to three decimal places).

d) The probability that there are more than three trucks in the system =
. 482 (round your response to three decimal places).

e) The total daily cost to the farmers of having their trucks tied up in the unloading process = $
1440 per day (round your response to the nearest whole number).

f) As mentioned, the cooperative uses the storage bin heavily only weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by % next year. It will cost $ to do so during the off-season.
The one year net cost/benefit to enlarge the storage area = $
2,080 (round your response to the nearest whole number).

**How do I solve for the $2080 for part f? I keep getting the daily cost as $720, but I'm not sure how to get to the net cost/benefit answer of $2080.

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The wheat harvesting season in the American Midwest is short, and farmers deliver their truckloads o...

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