Linear Programming

thingiverse

This is a representation of a linear optimization problem, also known as a linear program. This shape corresponds to an example known as the "Brewery Problem". Its objective is to maximize profit from the sale of three beers (light, dark, and ale), each requiring different combinations of three limited resources (barley, hops, and yeast). The polytope represents the feasible region, that is, amounts of the three beers that can be brewed without exhausting the resources. The plane represents the profit. Every point on that plane has the same level of profit. The optimal solution to the problem is where the plane intersects the polytope. There is more to it (see for example <a href="https://greenor.wordpress.com/2014/02/09/visualizing-lps-in-mathematica/">this post</a> ) but that is the basic idea.