mass production

Question

When the Rabbi said, Packaged products produced in a factory are not within the prohibition of Bishul Akum. (This applies to Sephardim & Ashkenazim.) Does this mean that it has to be davka a factory, or if a non-jew cooks in their private home something and sells it in a stand in front of their house does this also qualify? Also is there an issue of how much must food must be produced? Also does it matter if it packaged or not? Thanks