I am trying to solve a LP with simplex method which says like. Suppose,
Maximize $$10x_1+20x_2+20x_3$$
subject to
\begin{align} \tfrac{2}{3}x_1+4x_2+x_3&\leq 50&& (I)\\[0.5em] x_1 + 3x_2 + 4x_3 &\leq 130&& (A)\\[0.5em] x_1, x_2, x_3 &\ge 0&&(B) \end{align}
How are we supposed to solve this case?
I started by converting it to slack form, after which I have two new variables $s_1$ and $s_2$. I converted equations A and B to $s_1$ and $s_2$ form and then put non basic variables ($x_1$, $x_2$ and $x_3$) to zero to get a feasible solution.
After that, I have taken $x_1$ as pivot and changed it with S1 to optimize my value(which has improved a lot). But, now how will I choose my next pivot as I can only choose one to replace with $s_2$. I don't have a $s_3$ in this case to replace $x_3$.
So, in these cases, how should I proceed further? Should I replace $x_2$ with $s_2$ first and check optimized value of Z, and then repeat for $x_3$ with $s_2$ and then choose the best out of these? Or is there any other way?
Please help. Thanks in Advance