#### 3. Multiple Solutions or Alternate Optimal Solutions

While solving the LPP by simplex method, in the optimum simplex table, if the net evaluation *z*_{j} − *c*_{j} ≠ 0 for all non-basic variables, then the problem is said to have a unique optimal solution. On the other hand, if the net evaluation *z*_{j} − *c*_{j} = 0 for at least one non-basic variable, then the problem is said to have an alternative or infinite number of solutions.

In a graphical method if the optimal solution occurs at a vertex of the solution space, then the problem is said to have a unique optimal solution. If the optimum solution occurs on an edge of the solution space then the problem is said to have an alternative or infinite number of solutions.

**Example 5**

Solve the following LPP

Maximise ...