Linear programming instance/Online solver

Does anyone know what in this online linear programming problems solver AFTER clicking on the green button SOLVE is the meaning of the numbers below $$t$$, i.e. in the last column: $$\frac{1}{9},\frac{1}{10},\frac{1}{120}$$ in this instance of a linear program?

1 Answer

They seem like the numbers needed for the minimum ratio test, see this part of the simplex method description on Wikipedia.

• They say: "... A calculation shows that this occurs when the resulting value of the entering variable is at a minimum." Which calculation is it and if resulting variable OR rather the ratio? – user122424 Feb 28 '19 at 17:28
• @user122424 Look at "#4 Simplex table 1". If you choose $y_1$ as the pivot row, then for $b$ you get $-1/9$ in the second row, which corresponds to the solution $x_1=1/9$, $y_2=-1/9$, $x_2=x_3=x_4=y_1=0$. Since $y$ has to be nonnegative, that is not allowed. By choosing the smallest ratio, you ensure that you will not get a negative number in the $b$ column. The calculation is column $b$ divided by the column of the entering value (elementwise). – LinAlg Feb 28 '19 at 17:34
• I understand what you are saying but I do not follow how explicitly have you obtained $-1/9$ for $b$ and the other numbers in your comment's second row? – user122424 Feb 28 '19 at 18:22
• @user122424 could you create a pivot at the position I mentioned, carry out the row reduction steps, and share the resulting tableau so I can explain the numbers? – LinAlg Feb 28 '19 at 18:46
• I think that the pivot for our bad situation is in the #4 table the row with $y_1$ but I do not know which column? – user122424 Feb 28 '19 at 18:51