I wanted to get a formula for this problem, and also to know what "area" of math the problem would fall into. This is an abstraction of a system used within a game.
Suppose an item has four cost attributed to it, say the cost of its four materials A B C and D Item X cost: 10 A, 10 B, 20 C and 5D
You have different amount of materials A, B, C, and D in storage. You also have an exchange rate. Your exchange rate tell you how much of any material is needed to make another material. The fixed exchange rate is 2:1. This means you can convert 2 of one material into 1 of another material.
In storage I have 20,000 of material A, 30,000 of material B, 48,000 of material C and 50,000 of material D. I want to know two things:
I. How to make the MAXIMUM number of Item X's that I can, by utilizing the conversion process to change excess of one material into another. What's the formula? The answer for the MAX is of secondary importance.
II. How to bring all my material amount to equilibrium utilizing the conversion process. i.e. making A = B = C = D by converting higher amount materials into lower amounts until they are all the same. What's the formula? The answer of their balance point is of secondary importance.
For some reason this reminds me of "moments" and finding the center of polygon regions in the plane. In any case, I'd love to know the answer to my questions above, and what type of math this categorizes as. Thank you!