1. Special Cases in simplex method applications
Stat 261

2. Special cases Degeneracy Alternative (optima) Unbounded solutions
Infeasible solution

3. Degeneracy
If the optimal solution one or more of the original variables has‘0’ value,then this is called degenerate optimal solution. Example:

4. Alternative (optima)
If there is a ‘0’ under a non-basic variables in Z-row that’s means there are many solutions. Example:

5. Or by graphical method, if the slope z-row equal slope one of the constraints.

6. Unbounded solution
If under any non-basic , there are all minus or zero’s values , then the LP has unbounded solution.

8. Unbounded solution space with bounded objective value

10. Infeasible solution
Example: