in operation management Flow Process Measures

$4.$ Orange Juice Company 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 $6000$ kilograms. 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 $8000$ kilograms per hour. Assuming that oranges arrive continuously over

time, construct an inventory buildup diagram for Orange Juice Company. In order to

process all the oranges delivered during the day, how long must the plant operate on

peak days? Suppose that each truck holds about $1000$ 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?