Cocktail Optimization, an Integer Programming Problem

There's a fantastic website called Difford's Guide [1] that allows you to list the cocktail ingredients that you have and will then provide a long list of cocktails you can make (optionally allowing substitutions).

It is however a bit of a dangerous game for those who feel the urge to collect things, as it somewhat gamifies your drinks cabinet by telling you how many drinks you're missing out on unless you buy XYZ ingredient.

[1] https://www.diffordsguide.com

The problem with a French 75, which is a mighty fine cocktail, is that you'd have to drink an unhealthy number of them to finish a bottle of champagne before it went flat.

This has nothing to do with TFA and the math therein other than it's a cocktail on the list.

Writing a custom solver seems kind of absurd to me. There are 10s(/100s?) of open source ones out there. HiGHS in particular seems to be challenging the paid solvers with its LP improvements of late. But now I want to write my own.