I have a Linear Program with constrains of the form:
$$a_{11}x_1+a_{12}x_2+\ldots\le 0$$
$$a_{21}x_1+a_{22}x_2+\ldots\le 0$$
$$a_{31}x_1+a_{32}x_2+\ldots\le 0$$
My problem is that if I try to implement simplex I have problems in the tableau because every ratio is $0$. How can I face this problem? Is it possible to add a constant say $b$ to every constrain and also to the objective function?