# polyhedra – Size of integer variables around mean in an integer program

Consider the linear integer program

$$underline xinmathbb Z^n$$
$$Aunderline xleq b$$

where number of rows in $$A$$ is $$m$$ and number of bits to represent $$A$$ and $$b$$ is $$L$$.

1. Is there a bound on $$|underline x|_infty$$?

Denote $$x_{mean}$$ to be $$frac{sum_{i=1}^nunderline x_i}n$$.

1. Is there a bound in $$|underline x-x_{mean}|_infty$$?