The simplex algorithm always gives optimal solutions to linear programming problems.

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The simplex algorithm is a guaranteed method for finding optimal solutions to linear programming problems. It is based on the concept of moving along the edges of a polyhedron to reach the optimum point. However, in rare cases, degeneracy or cycling can occur, leading to suboptimal solutions. Nevertheless, the simplex algorithm is highly effective and widely used in practice.

The Simplex Algorithm Always Gives Optimal Solutions to Linear Programming