Subject to :
xi >= 0
With x4,x5,x6 the slack variables which we take as our basic variable and all equal to 20 for our full tableau implementation.
As you can see in the Z-row, all coefficients -10 and -12 are negative.
According to a video on Youtube (Dr.Salimian's) you take the most negative, in this case being -12, but when I do that I encounter the following problem : the coefficients of at least one of the basic variable (or their R.H.S) are negative. I calculated the low-ratios and took the smallest for the entering variable.
My question is : do we always take the most negative? And if we have two variable with the most negative ratios do we just pick one randomly?