Put out is typically closer to meaning of "release" in the sense of "making available", instead of "produce" in the sense of "create."
I've put out the food for the guests
I may have also cooked (created) the food, but that's a guess and not expressed in that statement.
It gets confusing because a meaning of produce is "make visible or available" - e.g.
Sally said she was hiding a secret note in her hand. I asked her to show it to me, and she produced a crumpled piece of paper.
but this does not mean Sally manufactured the piece of paper.
Do people say, for example, put out a number/an amount of rice, vegetables, cars, TVs, paper, wood pulp, steel?
What makes "put out" mean "create" in your example is context, which can override word meanings in English easily--especially with a small group of short English words with 15-20 or more meanings in the dictionary (other examples being set and get).
Because the list of items here seem to be bulk quantities or big stuff - e.g. rice, vegetables, cars - and aren't related to each other (e.g. it's not common/usual to buy vegetables and cars at the same store) it creates a context where "put out=create" makes sense.
If I'm working or talking about a factory, that's another example where context might lead someone to think "put out=create", e.g. "We put out tons and tons of paper a year."