No production unit ever has unlimited inputs. Its stock of raw material, the hours its machines can run, the size of its workforce and the room in its stores are all fixed for the month, yet a decision still has to be taken on how much of every product to turn out. In this report we look at how Operations Research (OR), and specifically linear programming (LP), supports that decision, using two published case studies of manufacturers in Nigeria. Solaja et al. (2019) work out a monthly output plan for a firm that makes animal feed, and Adebiyi, Amole and Soile (2014) choose the output mix for a paint maker selling five products. Each study is examined for its business setting, what the model tries to achieve, the limits and assumptions it uses, how it was solved, and what it does well or poorly. We then write down a general LP model for production planning. As our own contribution, we entered the numbers printed in both papers into a solver, solved them again, and ran several what-if cases on the feed data to see how the best plan shifts when the rules or the supply of inputs are changed.