Question

Big-M (describe process up to initial tableau and how to
recognize if infeasible) careful to distinguish between Max LP and
a Min LP

Answer 1

Description of the Big M Method

1. Modify the constraints so that the rhs of each constraint is nonnegative. Identify each constraint that is now an = or >= constraint.

2. Convert each inequality constraint to standard form (add a slack variable for <= constraints, add an excess variable for >= constraints).

3. For each >= or = constraint, add artificial variables. Add sign restriction ai >= 0.

4. Let M denote a very large positive number. Add (for each artificial variable) Ma_i to min problem objective functions or -Ma_i to max problem objective functions.

5. Since each artificial variable will be in the starting basis, all artificial variables must be eliminated from row 0 before beginning the simplex. Remembering M represents a very large number, solve the transformed problem by the simplex.

If all artificial variables in the optimal solution equal zero, the solution is optimal. If any artificial variables are positive in the optimal solution, the problem is infeasible.

Actually I have made the above slide for lecture purpose in very easy language so that anyone can understand easily. This example helps you to understand how we can create an initial table if we have given maximization or minimization problems.

Hope this will help you.

Ask if you have any quarries, thank you