Final answer:
The relevant range is likely to contain a linear relationship between costs and activities because it represents the range of activity where the assumption of linearity in cost behavior is considered valid.
Step-by-step explanation:
A linear relationship between costs and activities is most likely to be found within the relevant range. The relevant range is that range of activity where the assumption of linearity in cost behavior is valid for operations.
This means that within this range, we can expect total costs to change proportionately with changes in the level of activity. For example, a company's utility costs may have a linear relationship with hours of machinery operation but only within a certain range of hours (the relevant range), beyond which the costs may increase at a different rate.
Full capacity often involves complexities like overtime pay or equipment wear that can lead to non-linear cost behavior. Similarly, small-scale operations and the entire range of possible activity can also exhibit non-linearity due to fixed costs and other factors. Therefore, a linear approximation is typically not valid outside the relevant range.
The linear relationship between costs and activities is likely to be found in the relevant range of production. The relevant range refers to the range of activities within which the company expects its costs to behave in a linear manner.
Outside of the relevant range, costs may not follow a linear relationship due to factors like capacity constraints or economies of scale.