Your trucking company has been hired to move $250,000$ tons of manure from a feedlot. You

have analyzed the layout of the operation and have determined that you will use $5$ large dump

trucks. Each dump truck can legally operate with a gross weight of $80,000$ pounds $($Texas

Department of Transportation$).$The tare $($empty$)$ weight of each truck is $30,000$ pounds. Hence,

the maximum hauling load is $25$ tons. $($Use $20$ tons of manure per truck as an average load.$)$

You plan to use $3$ front$-$end loaders to load the trucks either directly from the lot or from one of

$3$ piles of $20$ tons each. Each front$-$end loader operator has been instructed that only one front$-$

end loader may be used to service a specific truck. However, more than one front$-$end loader may

work on the same $20-$ton piles. The following table gives the arrival and loading rates