nickarnosti.com/blog/lp_duality/
Today, my wife and I dropped my daughter off with grandma, so that we could have a “date morning.” My mom asked what our plans were. We said that we were going to a cafe, order some drinks, and talk about math. And that is exactly what we did. It was great. (I love my wife.) More specifically, I taught Amanda about linear programming, in a way that I wish I had been taught. I decided to reproduce our conversation in this blog post (extremely silly motivating example and all). For those who have seen linear programming duality before, there are no “new ideas” here. But if duality has always felt a bit like a magical black box, you may find this walkthrough illuminating. And for those who have not seen linear programming: if you have a solid grasp of 8th grade algebra, a pen, a piece of paper, and a little time, this post should be accessible to you! You run a small business that makes and sells things that float. More specifically, you make two products: boats and jetskis. These product