Orange Juice Inc. produces and markets fruit juice. During the orange harvest season, trucks bring oranges from the fields to the processing plant during a workday that runs from 7 A. M. to 6 P. M. On peak days, approximately 10,000 kilograms of oranges are trucked in per hour. Trucks dump their contents in a holding bin with a storage capacity of 6,000 kilo-grams. When the bin is full, incoming trucks must wait until it has sufficient available space. Aconveyor moves oranges from the bins to the processing plant. The plant is configured to deal with an average harvesting day, and maximum throughput (flow rate) is 8,000 kilograms per hour.
Assuming that oranges arrive continuously over time, construct an inventory buildup diagram for Orange Juice Inc. In order to process all the oranges delivered during the day, how long must the plant operate on peak days? (Assume, too, that because Orange Juice Inc. makes fresh juice, it cannot store oranges.) Assuming, finally, that each truck holds about 1,000 kilograms of oranges, at what point during the day must a truck first wait before unloading into the storage bin? What is the maximum amount of time that a truck must wait? How long will trucks wait, on average? Among trucks that do wait, how long is the average wait?