I am a young man studying economics on his own. In every microeconomics text I find, they teach you what a production function is, but they never show examples (or practice problems) on how one comes up with a production function of a firm on his/her own. Even in practice problems, a production function is already given. I can never find practice problems that help you practice finding an actual production function (ex: A firm has 3 ovens, 2 computers, 10 special extractors, and 15 workers in an olive oil plant. Find the production function for this firm).
I personally want to see how an economist makes up his/her own production function of a firm he/she is observing. I know this takes some sort of mathematical ability. I personally am not that good at modeling real life situations into functions yet (I am practicing that as well). This is why I want to practice this particular skill.
Can anyone please show me examples of this? Does anyone have any good websites or books that show great examples of this, along with practice problems? I have found nothing in almost every book/website I've found. Please help. Thank you.