Final answer:
A primary consideration in assigning a cost to a responsibility center is who can best control the change in that cost.
Step-by-step explanation:
A primary consideration in assigning a cost to a responsibility center is who can best control the change in that cost. When assigning a cost to a responsibility center, it is important to consider which individual or department has the ability to influence or manage that cost. This ensures that the cost is allocated to the responsible party.