Can it make sense to produce a product, even if it is at a loss?

Sometimes it makes sense to produce a product even if that product has a loss. This is because you can allocate the fixed costs to the losing product as well as the profitable product. If you were to allocate all fixed costs to the profitable product, it might not be profitable anymore! Of course, important to look at overall profit here, but you might find this to be the difference of overall loss or overall profit.