Can we say, in the context described below, that an outlay cost maximizes profit?
overlay costs are explicit costs that are associated with maintaining business activity (wages, materials, rents etc.). These costs are relevant and should be taken into account during the cost calculation process. In many cases, although some expenses are relevant, they are not simultaneously cost efficient (they do not deliver a certain level of outcome with minimum cost).
The scenario given here does not give us enough information to know whether profit is being maximized. It is surely true that profit will be maximized at some level of outlay cost, but there is no way to know what that level is.
In general, profit is maximized when a firm produces a quantity of product that allows the marginal cost to be equal to the marginal revenue. Marginal costs are the same thing as the outlay cost incurred for making the next unit of product. Therefore, when the marginal outlay cost is equal to the marginal revenue received, profit is maximized. However, given the information in the explanation above, we cannot tell if this is happening in this scenario. This means that there is no way to tell if profit is being maximized.