An earthmoving operation has available one loader with a $7-$cy heaped capacity bucket for filling $45\mathrm{.}9-$cy heaped capacity off$-$road trucks. All equipment operates at $50-$min hours. The loader produces a bucket fill factor of $90\%,$ and truck fill factor is $100\%.$ Loaders do not "short load." Loader cycle time is $0\mathrm{.}6$ min $($no travel$).$ Truck dump time is $0\mathrm{.}5$min $($includes maneuvering, dumping and turning$).$ The loaded trucks climb uphill through the following three sections and return empty downhill through the same sections. Trucks operate at rated load and empty weights.

$$ Calculate the number of cycles per loader to fill each truck.

$$ Calculate the number of trucks requied for each loader.

$$ Based on the number of trucks you determine, develop a curve for the $$/$cy production cost vs$.$ trucks curve for a range of $+/-2$ trucks. Use the following hourly rates $($including operator$)$ for each piece of equipment:

$7-$cy capacity loader $$175/$hr

$45\mathrm{.}9-$cy off road truck $$180/$hr$.$