Explanation:

Simplex procedure is an iterative method used to solve linear programming problems. In each iteration of the simplex procedure, a basic feasible solution (BFS) is obtained by setting non-basic variables to zero and solving for basic variables. The BFS is then used to determine the direction of movement towards the optimal solution.

When there are multiple BFS that provide the same optimal solution, the problem is said to be degenerate. In such cases, the simplex procedure may encounter tie situations where two or more non-basic variables have the same reduced cost. This means that the objective function value remains the same as we increase or decrease the value of any of these variables.

Tie situations in the simplex procedure can lead to cycling, where the algorithm keeps revisiting the same BFS without making any progress towards the optimal solution. This can result in an infinite loop, making it impossible to find the optimal solution.

However, leaving variables in the basis during the simplex procedure can help to break ties and prevent cycling. By leaving non-basic variables in the basis, we can introduce more constraints and reduce the number of possible BFS. This can help to ensure that the simplex procedure converges to the optimal solution without cycling.

Therefore, tie situations in the simplex procedure do not necessarily imply optimality, cycling, or no solution. Instead, they indicate degeneracy, which can be resolved by leaving variables in the basis.