# Minimum value for a group of variables in linear programming

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 $$m=3, n=0, p=0$$.

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 : $$\sum_{i} x_i^A \ge 1 \\ \sum_{i} x_i^B \ge 1 \\ x_i^A, x_i^B \in \mathbb{N}$$