No, the relaxed constraint was not the cause of both infeasibility and unboundedness.
While the constraint was the direct cause of the infeasibility (because removing it allowed solutions to exist), it was actually acting as a crucial "ceiling" or "shield" that prevented the problem from exploding to infinity. Removing it didn't create the unboundedness—it merely exposed an underlying structural flaw in the rest of your model.

No. Relaxing the constraint may remove the conflict causing infeasibility, but it can also remove a limit that was preventing the objective from improving indefinitely. Thus, infeasibility is caused by conflicting constraints, while unboundedness is caused by insufficient constraints to limit the objective.

No. The relaxed constraint may have been responsible for the infeasibility, because relaxing it can create a nonempty feasible region. However, unboundedness is a separate issue: it occurs when the new feasible region extends indefinitely in a direction that improves the objective. Thus, the same constraint may have contributed to the original infeasibility and its relaxation may expose unboundedness, but these are different properties requiring different reasoning—one concerns whether any feasible solution exists, while the other concerns whether the objective has a finite optimum.

No, the relaxed constraint is not necessarily the “cause” of both. Infeasibility means the original constraints had no common feasible solution, while unboundedness means the relaxed model has a feasible region that allows the objective to improve indefinitely; these are separate properties that require different analyses.

No. The relaxed constraint may have caused the original infeasibility, but it is not necessarily the cause of unboundedness. Infeasibility means there was no feasible solution before the relaxation, while unboundedness means the feasible region became unlimited in a direction that improves the objective. These are different properties and require separate analysis.