We call a linear programming $Ax=b$ combinatorial if the size of entries of matrix $A$ is bounded by a polynomial of dimension of the LP problem. The size of a rational number is described as the length of its binary representation.

What I am thinking is that any entry size is a polynomial of the LP dimension. In other words,    size($a_{ij}$) = size($a_{ij}$) * $m^0$ $n^0$ where size of LP is $m\times n$.

In my viewpoint any LP is combinatorial. I must think wrongly but why?