How can I modelize a weekly menu and minimize the total number of ingredients it contains

Question

Hi and many thanks for reading this question.

I want to create an algorithm that will minimize the total number of ingredients that are in a weekly menu. A menu is made of several recipes, for simplicity let's say 5 recipes. Recipes are randomly selected from a database of many recipes. Each recipe has ingredients that can be identical or different.

1. I would like your help to modelize this problem so it can be optimized.
2. If you have any idea of what type of proble this is (NP Complex?) that could also help me going in the right direction.

Thanks for your help.

Answer 1

1. Since recipes are randomly selected, a menu (5 recipes) is also randomly selected from database. Hence, there is no need (or way) to optimize the outcome.

2. This is not an NP-complex problem. It has complexity O(1), or maybe O(0).