Input by hand (or generate randomly) a problem to solve. Ignoring the
integrality constraint on the variables, solve the so-called LP-relaxation.

After the relaxation is solved, if by luck all of the x_{j}
variables are integer, then you are done. Click the "Optimal" button to
confirm that you have found the optimal solution.

If in the optimal dictionary some of the
x_{j}
variables are not integers, then click "Add Cuts" to generate appropriate
Gomory cuts as new constraints. The current solution will be infeasible with
respect to these constraints.
Use the dual simplex method to solve to optimality.

If the new optimal solution has all integer values for the
x_{j}
then again you are done.
If not, then click "Add Cuts" again and repeat. Keep repeating until the
optimal solution has all integer values for the
x_{j}
variables.

NOTE: The slack variables introduced as "cuts" have a pair of integers as
subscripts. The first integer represents the number of times "Add Cuts" has
been invoked and the second integer is the j-index of the variable
x_{j} that is the basic variable in this row.

Acknowledgement: I'd like to thank Hande Benson for coding up the first version
of this implemention of the Gomory Cut algorithm.