Question

In: Statistics and Probability

OJ Inc. produces and markets fruit juice. During the harvesting season, trucks bring oranges from the...

OJ Inc. produces and markets fruit juice. During the harvesting season, trucks bring oranges from the fields to the processing plant each day during 7 A.M. to 6 P.M. On peak days, approximately 10,000 kg of oranges are trucked in every hour (assume that this occurs at a constant rate, so the size of individual trucks doesn’t matter). Trucks must dump their contents in a holding bin with a storage capacity of 6,000 kg. When the bin is full, incoming trucks must wait until the bin has available space. The plant is configured such that the processing rate is 8,000 kg per hour. Assume that the plant must keep processing until all oranges that arrive on any day are processed.

Construct an inventory buildup diagram for OJ Inc. to answer the following questions.

12. How many hours after 7 A.M. do the trucks first start waiting?

13. What is the maximum quantity of oranges, in kgs, that is waiting on trucks (to be dumped into the bins)?

14. How many hours after 7 A.M. does the maximum quantity of oranges that is waiting on trucks (to be dumped into the bins) accumulate (in hours)?

15. How many hours after 7 A.M. do the trucks stop waiting?

16. How many hours after 7 A.M. does the factory stop processing for the day?

Expert Solution

Based on the given data, an inventory build up diagram is constructed as below

Inventory per every one hour = 10000-8000 = 2000

therefore, total inventory at the end i.e., 6 pm = 2000*11 = 22,000

and the stored inventory is utilized after 6pm for 22000/8000 hrs = 2.75 hours

16) therefore, the whole production will be finished by 8:45 pm

12)inventory build up for every 1 hr = 2000

and the bin capacity = 6000

==> the first truck will start waiting after 6000/2000 hrs = 3 hrs

14) the last truck that enters at 6pm waits the longest, and it has to wait for t hrs in the queue, t can be calculated as below

22000 = 8000*t+6000 ==> t = 2hrs

therefore, the longest wait time for any truck is 2 hrs, therefore the trucks will be free after 8pm

15) Therefore, the trucks will stop waiting after 8pm

orchestra answered 2 years ago

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