Could a government work like this?

Could there be a government that produces and sells products, and uses the profit for the community. Say like the government sold food, or clothes or built electical power plants or water purification plants, and sold just things of that nature, while making profit for the community. You could create profit caps so people dont get ripped off by the government, and more importantly i bet you could lower taxes tremendously and keep public services at a pretty high standard. Do think a government that runs like this could work?