I have this LP-problem which I need to solve using simplex calculations.
$$ \max Z = 12x_1 + 18x_2 + 10x_3 $$
when,
\begin{align} 2x_1 + 3x_2 + 4x_3 &= 50\\ -x_1 + x_2 + x_3 &= 0\\ -x_2 + \frac32x_3 & = 0\\ x_1 , x_2 , x_3 & > 0\\ \end{align}
How do I solve this? I'm quite confused about the constraint terms 2 & 3 which are equal to $0$. Do this even have possible solutions?
I get $Z = 300$ as a result of only one iteration. In my results $x_2$ will be entering the set of basic variables and replacing $s_2$ (s2 is slack variable for the constraint 2). But I think this is not right way to do it.
Starting table (pic1).
After first iteration results (pic2).
cj-zj values are all <0 which shows that we are "done" and we found the best alternative values.