Minimum value for a group of variables in linear programming

Question

I want to use linear programming to assign weights to a number of groups of variables.

Let's assume we have group $A$ with $x,y,$ and $z$ and group $B$ with $m,n,$ and $p$.

Is it possible to define constraints so that at least one of the variables from each group gets a weight larger than zero?

A feasible solution wout be $x=2,y=0,z=0$ and $m=3, n=0, p=0$.

Answer 1

I am assuming the weights are integers.

Let $x_i^A$ denote the weight assigned to item $i$ from group $A$ and $x_i^B$ denote the weight assigned to item $i$ from group $B$.

You need the following constraints : $$ \sum_{i} x_i^A \ge 1 \\ \sum_{i} x_i^B \ge 1 \\ x_i^A, x_i^B \in \mathbb{N} $$