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Formulate the linear programming problem in standard form, where all the constraints are inequalities with non-negative right-hand sides, and the objective function is to be maximized.

Conduct the pivot operation to transform the pivot element to 1 and create zeros in the rest of the pivot column using row operations.

If the current tableau is not optimal, repeat Steps 3 to 7 using the updated simplex tableau until an optimal solution is obtained or the problem is found to be unbounded.

Locate the pivot row by dividing the rightmost column values by their corresponding positive values in the pivot column, choosing the row with the smallest non-negative quotient.

Convert the standard form into an initial simplex tableau by introducing slack, surplus, and artificial variables as necessary to handle inequalities.

Determine the entering variable by identifying the column in the simplex tableau that corresponds to the most negative coefficient in the objective function row.

After pivoting, update the simplex tableau to reflect the new basic feasible solution (new values in the rows and columns according to the row operations performed).

Verify if the current simplex tableau represents the optimal solution by checking if there are no negative coefficients in the objective function row, except possibly in the artificial variable columns.

If there is more than one zero in the objective function row, corresponding to non-basic variables, there may be alternative optimal solutions to evaluate.