Maximize $$ z = 2x_1 -x_2 +x_3$$
Subject to constraints $$2x_1 + 3x_2 -5x_3 \ge 4$$ $$-x_1 +9x_2 -x_3 \ge 3$$ $$4x_1 +6x_2 +3x_3 \le 8$$ And $x_1, x_2, x_3 \ge 0$
I managed to solve this through simplex method(by 2 stage method) but I was asked solve it using dual simplex method, I found out that this cannot be solved by dual simplex since it doesn't meet the maximization optimality condition here which is the reduced costs in the z-row(or the values in the z-row in the initial table) must be always lesser than $0$ which is not the case here as coefficient of $x_2$ is 2 in the z-row.
Still our teacher says it can be solved by introducing another constraint which is $x_1 + x_3 \le M$ (where M is sufficiently large), now I am at a loss how to proceed further ?
I know the answer will be quiet huge and time taking but any type of help will be greatly appreciated.