The correct answer is option 'D': The simplex algorithm is an iterative procedure.

The simplex method is a widely used algorithm for solving linear programming problems. It was developed by George Dantzig in the late 1940s and has since become a fundamental tool in optimization theory and operations research.

Iterative Procedure:
The simplex algorithm is an iterative procedure, meaning it applies a set of steps repeatedly until a solution is found or a specified stopping criterion is met. It starts with an initial feasible solution and then iteratively improves the solution until an optimal solution is reached.

Steps of the Simplex Method:
1. Formulate the linear programming problem in standard form, which involves writing the objective function and the constraints as a system of linear equations or inequalities.
2. Identify an initial feasible solution by introducing slack or surplus variables to convert the inequalities into equations.
3. Choose an entering variable, which is a non-basic variable that can be increased to improve the objective function value.
4. Choose a leaving variable, which is a basic variable that can be decreased to maintain feasibility.
5. Update the basic and non-basic variables using a pivot operation, which essentially swaps the entering and leaving variables.
6. Repeat steps 3-5 until an optimal solution is reached, i.e., no non-basic variable can be increased to further improve the objective function value.
7. The final solution will have all non-basic variables set to zero, and the values of the basic variables represent the optimal solution.

Advantages of the Simplex Method:
- The simplex algorithm is efficient and can solve linear programming problems with a large number of variables and constraints.
- It guarantees convergence to an optimal solution if one exists.
- It can handle problems with both equality and inequality constraints.
- It provides sensitivity analysis, allowing decision-makers to understand how changes in the problem parameters affect the optimal solution.

Limitations of the Simplex Method:
- The simplex method may not terminate if the problem is unbounded, meaning there is no upper limit on the objective function value.
- It may also fail to converge if the problem is degenerate, meaning there are multiple optimal solutions.
- The simplex method can become computationally expensive for problems with a large number of variables and constraints.

In conclusion, the simplex algorithm is an iterative procedure used to solve linear programming problems. It is a powerful tool for optimization and can handle problems with both equality and inequality constraints. However, it may have limitations in terms of termination and computational complexity for certain problem types.