I have a linear programming problem

min $c^T x$

$Ax\leq b$

However, in my problem, $A$ constains also some variabes $y$, e.g.

A= y1 4

  3  y2

The question is that I want to find evaluation of $y$ such that the solution of LP is positive.

This question is different than normal formulation of parametric LP, and I do not want to simply use nonlinear programing. Any good solution?