Conditional constraint in optimization not using integer or non-linear equation

Question

Suppose there are 2 non-negative variables xin and xout, and I'd like to make more than one of two as 0.

so the example : (xin, xout) = (0,0), (1,0), (0,2) are okay but (3,4) is not.

Can I formulate this not using integer or non-linear equation (Keeping it LP) and not modifying objective function?

Answer 1

Sorry, this cannot be formulated as a pure LP.

One way to prove this is to observe that LPs have a convex feasible region. That means that if (0,1) and (1,0) are feasible, so is (0.5,0.5). But you want to forbid this last solution.