I must solve that set of inequalities (maximization): $$2x_1 + 3x_2 + 4x_3 \le 9$$ $$5/2x_1 + 10/3x_2 + 6x_3 \gt 10 $$ $$x_1 \ge 1$$ $$x_1 \le 2$$ $$x_3 \le 2$$ $$\text{max } 5/2x_1 + 10/3x_2 + 6x_3$$
It is a one of step in branch and bound method. As you can see expression which should be maximized is same as one of the inequality. When I try to solve this using dual simplex method it break when all ratio (domain/{row_with_more_negative_rhs}) equals 0. Then i am a beginner in linear programming so should I deal with it on different way? I try to follow examples and docs from internet but it doesn't help me.
That is part of Cutting Stock Problem solver.
EDIT Simplex table: $$ \left[ \begin{array}{cccccccc|c} 2&3&4&1&0&0&0&0&9\\ 5/2&10/3&6&0&-1&0&0&0&{10+\lambda}\\ 1&0&0&0&0&-1&0&0&1\\ 1&0&0&0&0&0&1&0&2\\ 0&0&1&0&0&0&0&1&2\\ \hline 5/2&10/3&6&0&0&0&0&0&0\\ \end{array} \right] $$
$\lambda \in (0,1]$