In a simplex problem, if the most negative integer lies in the column of slack variables, can that column be used as pivot column?
In a simplex problem, the choice of pivot column depends on whether the most negative value lies within the column of slack variables.
To determine the pivot column, you need to identify the column with the most negative entry in the bottom row (also known as the objective row) of the simplex tableau. This entry represents the coefficient of the basic variable that can be increased to achieve a better objective value.
If the most negative value lies in the column of slack variables, then the associated basic variable is already at its lower bound and cannot be increased any further. In this case, the column of slack variables cannot be used as a pivot column.
To find a suitable pivot column, you need to look for a column in the tableau where all the entries are positive, except for the bottom row that contains the objective function coefficients. If there are multiple columns with negative entries in the bottom row, the one with the most negative value becomes the pivot column.
Once you have identified the pivot column, you can proceed with finding the pivot row, performing the pivot operation, and updating the simplex tableau to move towards the optimal solution.