Simplex method in matrix form with the big $M$ method?

Question

If I have one constraint $3_{x1}+2_{x2}=18$ in a maximize problem you need to fulfil $AX\le b$
what should I do to fit the condition ?
What I think is:
$3_{x1}+2_{x2}\le 18$ and
$3_{x1}+2_{x2}\ge 18$ becomes $-3_{x1}-2_{x2}\le -18.$
In tableau form we can use the big $M$ method to fix this but in matrix form this is not quite right.

Answer 1

First thing to know is the number of decision variables and number of constraints involved in your problem. I don't see any reason to split equality equations into two inequalities. One can directly add an artificial variable in the equality constraint $3x_1+2x_2=18$ and proceed with Big M or Two Phase method to obtain the solution.