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Orange Juice Inc. produces and markets fruit juice. During the orange harvest season, trucks bring oranges from the fields to the processing plant...
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 7am to 6pm. On peak days, approximately 12 tons of oranges are trucked in every hour (i.e. inflow is continuous and constant from 7am to 6pm). Trucks dump their contents in a holding bin with a storage capacity of 7 tons. When the bin is full, incoming trucks must wait until it has sufficient available space. A conveyor moves oranges from the bins to the processing plant. The plant is configured to deal with an average harvesting day, and maximum throughput is 10 tons per hour.
Assuming the oranges arrive continuously over time and all oranges must be processed the day they are picked to ensure freshness. How many hours are there between the first truck being forced to wait (i.e. inventory equals bin capacity) and the last truck being allowed to leave (i.e. the last orange is delivered from the truck into the bin)?
