Final answer:
The statement is true; variable consumption rates for material resources mean that the amount and cost of the resources change when the duration of the associated task changes. This is because variable costs, like labor and raw materials, vary with output levels and thus with task duration.
Step-by-step explanation:
When a variable consumption rate is assigned to a material resource in a project management context, and the duration of the task to which it is assigned changes, the calculated amount and cost of the material resource do indeed change. This statement is true. Variable costs, such as labor and raw materials, fluctuate with the level of output. In a scenario where the production rate of a resource is variable and not steady, increasing the duration may lead to using more resources, hence increasing the total cost. Additionally, when a resource has a consumption pattern that follows a peak and then declines, as is realistic with many finite resources like fossil fuels, the changes in task duration would impact the resource's consumption rate and the total cost.
In the context of production and project management, tracking variable costs is crucial because these costs will dictate the level of profitability and cost management effectiveness. Cost planning must account for variations in task duration, which will directly affect the consumption and cost of materials used.