Fast food restaurants are in the business of making a profit, so I would hope that the manager would be wise enough to quickly assess the situation, including available outside resources, and do their best to accommodate the order. If it is a chain and there are other sister establishments in the area, even if it is owned by someone else, they can call on them to help with the replenishing of supplies.
There comes a point though where they would need to realize that they could not fulfill one large order that would prevent them from accommodating other customers. In this case, I would hope that the manager would inform the customer that they can handle X amount of the order, and ___ location X miles away can take care of the rest if they want it faster. If they don’t want to drive to another location, it take X hours to fill the order. That way, the customer has the choice to opt for either of these choices or cancel the order altogether.
Or maybe the manager could ask if they all need to be hamburgers? They might be able to accommodate the order if X are burgers and X are chicken sandwiches.