In this paper we shall deal with the following nonconvex optimization problem: $(P)$ Minimize $c^Tz$, subject to $z\in D$ and $z_i=x_iy_i$ for all $i=1,\dots,p\leq n, x\in X, y\in S$,  where $D, S$ are polyhedrons in $\mathbb R^n$, $\mathbb R^p$ respectively, $X=\{x\in\mathbb R^p\,|\, 0 < a\leq x\leq A\}$; $a, A$ are $p$-vectors; $c$ is an $n$-vector. It is shown that $(P)$ can be reduced to a linear program whose constraints can explicitly be given in some special cases.