I read that Full costing because it's gross profit and profit is always the same, no matter which overhead allocation basis is chosen, therefore it failed to identify relevant and irrelevant cost, hence it is not suitable for decision making at a firm level. However, I failed to see the connection between relevant cost and full costing system, because relevant cost, even with non-production overhead, if it's affected by let's say the purchase of new machine result in a decrease cost of non-production overhead, then this effect is still accounted for and will be part of the calculation. Whereas full costing discarded the non-production cost, and focus only on the cost that contributes to the production. So saying that failed to identify relevant and irrelevant cost does not seem accurate for me, hence the only downside I can say about full-costing is the arbitrary costing system is flawed. I am not going against sth that is well-regarded by the accounting community, but can anyone tell me why full costing failed to identify relevant and irrelevant costs?