The larger the supply, the lower the price. Therefore, the more thneeds you (the firm) produce, the less you'll be able to sell each one for. Traditional sense says that as long as there are people who will buy them, you should always make more thneeds! But given profit is quantity * (selling price - costs), as price drops, you may eventually reach a point where profit decreases the more thneeds you make.
If and when this happens depends on the shape of the supply-demand curve, rather than using the simplified linear ones you learn about in early university economics.
Does this happen? Is there a "supply-induced-price-drop-compensated" ideal quantity to produce to maximize profit?