If $f(A,b,c)$ is the optimal value of a linear program

$\min c.x$

subject to $A.x \leq b ; x \geq 0.$

Does $f(A,b,c)$ have a piecewise polynomial/rational upper bound in $(A,b,c)$ on the domain of points in which the optimal value is well-defined/finite? Here, we assume that the matrix $A$ is an $m \times n$ matrix.