I hope someone can help me. I am trying to get a head start on uni this year by learning some linear programming from a book, but it is getting confusing.
I have read that you pick the leaving variable by minimising the ratio $\{\frac{b_i}{a_{ij}} : a_{ij}>0\}$
However by doing this I seem to be going round in circles (I am presuming it is okay to reverse the leaving and entering variables on the next iteration - I read this on another question here)
So I have to following:
$ z=-\frac{65}{9}-\frac{8}{9}x_1-s_1+\frac{13}{9}s_2+\frac{4}{9}x_0$
$x_3=\frac{65}{9}+\frac{8}{9}+s_1-\frac{13}{9}s_2-\frac{4}{9}x_0$
$x_2=\frac{4}{9}-\frac{2}{9}x_1+0s_1+\frac{1}{9}s_2+\frac{1}{9}x_0 $
Is it wrong that $z$ is just $-x_3$?
I picked $s_2$ to enter and $x_2$ to leave as this is the only basic variable with a positive coefficient of $s_2$. But then on the next iteration I needed to pick $x_2$ to enter and $s_2$ to exit the basis. Have I done this wrong?
As an aside (another question - hope this is okay), if I am solving an auxiliary problem and have negatives, do I choose to the leaving variable is the one that minimises or maximises the ratio $\{\frac{b_i}{a_{ij}} : a_{ij}<0\}$?
I am so confused, I hope someone can help me. I realise it is not that important as I will learn how to do it properly in lectures, but I am really bored and need maths to do to keep me going for the next three weeks!
TIA