For the firm's cost minimization problem, one of the key assumptions for each input is that:

A) marginal product is constant.
B) marginal product is increasing at a decreasing rate.
C) marginal product is increasing at an increasing rate.
D) marginal product is decreasing at an increasing rate.

The assumption that the marginal product of an input is increasing at a decreasing rate is consistent with the law of diminishing marginal returns. This principle states that as the quantity of an input increases, the additional output generated from an additional unit of input will eventually decrease. This assumption is crucial for the cost minimization problem because it reflects realistic production conditions where, beyond a certain point, adding more of an input yields progressively smaller increases in output.