[Bob Haugen #14](https://forum.azimuthproject.org/discussion/comment/17809/#Comment_17809):

> Like, the Oglalla Aquifer has x amount of water that regenerates with y rate. How much water can be pumped out per year for human uses, e.g. irrigated farming?

I don't think this is covered in the book.

For a simple model like this, you use [linear programming](https://en.wikipedia.org/wiki/Linear_programming). There are a number of elegant theorems regarding linear programming, in particular [duality theorems](http://web.mit.edu/15.053/www/AMP-Chapter-04.pdf).

I couldn't find much investigation into the connection of category theory to linear programming. There's [Chavez (1989)](https://www.sciencedirect.com/science/article/pii/0097316589900319) who develops the category of \\(LP^\ast\\). There's also [Hochstattler et al. (1999)](http://www.kurims.kyoto-u.ac.jp/EMIS/journals/CMUC/pdf/cmuc9903/honeset.pdf).

Linear programming is a special class of convex optimization problems. There is bleeding edge research by [Conal Elliot (2018)](https://arxiv.org/abs/1804.00746) and [Brendan Fong (2017)](https://www.researchgate.net/publication/321347450_Backprop_as_Functor_A_compositional_perspective_on_supervised_learning) on connecting gradient descent techniques for solving these to category theory.

> Like, the Oglalla Aquifer has x amount of water that regenerates with y rate. How much water can be pumped out per year for human uses, e.g. irrigated farming?

I don't think this is covered in the book.

For a simple model like this, you use [linear programming](https://en.wikipedia.org/wiki/Linear_programming). There are a number of elegant theorems regarding linear programming, in particular [duality theorems](http://web.mit.edu/15.053/www/AMP-Chapter-04.pdf).

I couldn't find much investigation into the connection of category theory to linear programming. There's [Chavez (1989)](https://www.sciencedirect.com/science/article/pii/0097316589900319) who develops the category of \\(LP^\ast\\). There's also [Hochstattler et al. (1999)](http://www.kurims.kyoto-u.ac.jp/EMIS/journals/CMUC/pdf/cmuc9903/honeset.pdf).

Linear programming is a special class of convex optimization problems. There is bleeding edge research by [Conal Elliot (2018)](https://arxiv.org/abs/1804.00746) and [Brendan Fong (2017)](https://www.researchgate.net/publication/321347450_Backprop_as_Functor_A_compositional_perspective_on_supervised_learning) on connecting gradient descent techniques for solving these to category theory.