# How to efficiently formulate constraints in a linear programming model?

I'm studying a few example cases of LP from my book to practice but I am having a lot of difficulties when it comes to formulating the constraints for my model.

I have particular problems with two constraints in the example I am at at the moment. (Maximization problem with 2 variables, in case it's relevant)

"There must be at least 10 units of each product"


And

"The amount of product X must be at least as high as the amount of product Y"


So for the first one, I know that I could easily just make 2 separate constraints, where

X >= 10


and another one where

Y >= 10


but I was wondering if there was a better way to do it, so as to merge both of them into one single constraint?

For the second one, I formulated

X - Y >= 0

but I'm not sure if my logic is correct there, and I was avoiding using X >= Y since I don't like the idea of having a constraint that isn't crystal clear (I don't know how much Y will be, so to me it seems like an unreliable way to formulate it)

• Everything is OK and you are unnecessarily worried. You can formulate all you want as long as your constraints are linear (in)equalities and everything is crystal clear. (Unless the problem explicitly expects you to fit it into some standard form) – Michal Adamaszek Nov 16 '20 at 7:45