You weren’t kidding when you said “there is no unique solution to this problem”. In fact, there is a 3-dimensional space of possible solutions :)

Consider this. Even if you drop the (kmin, kmax) business and simply require Ax + By + Cz = K, then for ANY choice of A and B you can find a C satisfying the equation exactly. A trivial example: suppose A and B equal 0; then C = K / z.

In order to narrow down the search further, you must specify some restrictions on the values of A, B, and C, and/or tell us more about what you mean by “best”.

Hey,

Given a input data set (x, y, z, Kmin, Kmax) that satisfies the following euqations

Ax + By + Cz > Kmin

Ax + By + Cz < Kmax

is there a way to find A, B, and C.

I understand that there is no unique solution to this problem. But what I am looking for is a possibly the best solution (with tolerance).

Thanks!