What is the outcome when a model demonstrates infeasibility?

When a linear programming model demonstrates infeasibility, it means that there are no combinations of decision variable values that can satisfy all of the given constraints simultaneously. This condition occurs when the constraints imposed on the model conflict to such an extent that it becomes impossible to find a feasible solution.

For example, if one constraint requires that a value must be greater than a certain amount while another constraint requires that it must be less than that same amount, it creates a contradiction. Thus, within the feasible region defined by the constraints, there simply isn't any point (or combination of variable values) that can satisfy all of them at the same time.

In contrast, if there were valid solutions that meet all constraints, or if only some constraints could be satisfied, the model would be considered feasible. The existence of adjustable decision variables does not negate the infeasibility; indeed, adjusting those variables still wouldn't lead to a valid solution that satisfies all constraints. Therefore, the statement that no valid solutions exist that satisfy the constraints accurately encapsulates the meaning of infeasibility in linear programming.