When applying the **Simplex Method** to calculate the minimum coefficient or feasibility condition, if there is a tie for the minimum ratio or minimum coefficient it can be broken arbitrarily. In this instance, at least one basic variable will become **zero** in the following iteration, confirming that in this instance the new solution is ** degenerate. **The practical implication of this condition indicates that the model has at least one redundant constraint.

**Degenerate Optimal Solution**

Let’s consider the following Linear Programming model which we will solve using the **Simplex Method **and which we will also represent graphically with **Geogebra:**

We put the above problem in its minimized standard form, adding and , as slack variables for constraints 1 and 2, respectively.

Which produces the following **Simplex Method** initial tableau:

To facilitate the fast convergence of the algorithm we select as the entering variable. Next we calculate the feasibility criteria (smallest coefficient): (if a tie exists we arbitrarily select variable as the variable that leaves the basis. Then we update the tableau:

Now enters the basis. The feasibility criteria determines that: leaves the basis. A new iteration is made:

The degenerate optimal solution is reached for the linear problem. Note that . As this is a two-dimensional problem, the solution is ** overdetermined** and one of the constraints is

**just like the following graph confirms:**

*redundant*In ** practice **knowing that some resources (like those associated with a constraint) are superfluous can be useful during the implementation of a solution. From a

**point of view, the degeneration has two implications: it produces the cycling or circling phenomenon (it’s possible that the Simplex Method repeats a series of iterations without ever improving the value of the objective function and the calculations are interminable, as can be observed in the previous example); the second theoretical aspect arises when iterations 1 and 2 are examined. Although they differ in the classification of basic and nonbasic variables, both produce identical values for all variables and for the objective value .**

*theoretical*

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