When a firm is making the decision about whether to shut down, it considers only one kind of cost. In addition, it considers one aspect of revenue.
The only cost that a firm should consider when making this decision is its average variable cost. Its total costs do not matter and neither do its fixed costs. What the firm must determine is whether its average variable costs are higher than the marginal revenue that it can receive if it stays open. If the average variable costs are higher, it should shut down. If the average variable costs are lower than the marginal revenue, it should remain open even if it is losing money.
To see why this is so, let us look at the following hypothetical situation. Let us imagine there is a hotel whose average fixed costs per room per night (things like the mortgage on the building, taxes, and insurance) are $100. Let us then imagine the hotel incurs $90 in average variable costs per room per night. These are things like maid service and internet usage. Thus, it costs the hotel $190 per occupied room per night to stay open.
So, let us see what happens if the hotel can only charge $95 per room per night during its offseason. Each time it rents a room, it loses $95 ($190 in total costs minus $95 in marginal revenue equals $95 lost). It seems obvious that the hotel should close. But let us see what happens if it closes. It no longer has to pay the $90 in average variable costs. However, it still loses $100 per night due to its fixed costs. Thus, the hotel is actually better off if it stays open. It will lose money, but it will not lose as much as it would by closing.
Thus, a firm should only consider average variable costs and marginal revenue when deciding whether to shut down.