Final answer:
The direct answer to the assignment problem's question is that every changing cell (variable) in the optimal solution will have a value of either zero or one, representing whether a resource is not assigned or assigned to a task, respectively. This is a standard binary assignment scenario common in mathematical optimization problems.
Step-by-step explanation:
The subject question relates to assignment problems in mathematics, specifically in operations research or optimization fields. Assignment problems typically involve assigning resources to tasks in the most efficient way possible. The optimal solution implies that each resource (or 'changing cell') is assigned to exactly one task without any overlap, meaning the values in the solution matrix are either 0 or 1, where 1 indicates an assignment and 0 indicates no assignment.
An optimal solution to an assignment problem usually means that each changing cell, or variable, will have a value of either 0 or 1. This binary outcome is inherent in the nature of assignment problems, where resources are fully assigned (1) or not at all (0) to tasks. The context provided seems to discuss quantum numbers and their allowed values, which is a concept from physics, and does not directly relate to standard assignment problems in mathematics. However, in the realm of assignment problems, the objective is to minimize (or maximize, depending on the problem) the total cost or maximize the efficiency of the resource allocation.