Let be the following linear program:
\begin{equation*} \begin{cases} \max f(x_1,x_2) =3x_1+2x_2\\ 5x_1 + 2x_2 \ge 8\\ x_1 - x_2 \le 1\\ x_1 + x_2 \le 3\\ x_1,x_2\ge 0 \end{cases} \end{equation*}
I know how to graphically guess where a starting point is but how to find it with the Simplex algorithm?
Here I graphically guess that we would strat from the bottom or the left, but it's only a guess as fas as we are under a $\max$ condition.
After having put in place the begining of the Simplex algorithm, I have:
$$ \begin{array}{llllll} x_3= 8& -5X_1 &-2X_2 & & &\\ x_4= 1& - X_1& +X_2& &\\ x_5= 3& -X_1 & -X_2 & & &\\ \hline z= & 3X_1 & + 2X_2 \end{array} $$
but how to find the starting point from here? I only know that the variable about to come is $X_1$ because it has the greatest coefficient...