Name what stays fixed before writing a model. For identical workers with constant equal productivity, output in a fixed time is directly proportional to worker count. For a fixed job, completion time is inversely proportional to worker count, provided the work can be shared without delays. Example In one shift, 12 workers make 96 identical items. Under the same conditions, 7 workers make 9612 x 7=56 items. A fixed job takes 8 workers 15 days. The work requirement is 8 x 15=120 worker-days. With 10 equally productive workers it takes 12010=12 days. The model may fail if equipment limits output, workers have different rates, or the job cannot be divided. More workers should shorten a fixed job; use that direction check before accepting the result.

Name what stays fixed before writing a model. For identical workers with constant equal productivity, output in a fixed time is directly proportional to worker count. For a fixed job, completion time is inversely proportional to worker count, provided the work can be shared without delays.

In one shift, \(12\) workers make \(96\) identical items. Under the same conditions, \(7\) workers make \(\dfrac{96}{12}\times7=56\) items.

A fixed job takes \(8\) workers \(15\) days. The work requirement is \(8\times15=120\) worker-days. With \(10\) equally productive workers it takes \(\dfrac{120}{10}=12\) days.

The model may fail if equipment limits output, workers have different rates, or the job cannot be divided. More workers should shorten a fixed job; use that direction check before accepting the result.

Choosing and using a proportion model

Choosing and using a proportion model