Simplex method is an iterative mathematical optimization technique that is widely used to solve linear programming problems. The method involves moving from one corner point of the feasible region to another corner point in a systematic way until the optimal solution is reached. However, there are some types of solutions that cannot be obtained using the simplex method.

Not Possible Solution Types in Simplex Method:

1. Infeasible solution: An infeasible solution is a solution that does not satisfy all the constraints of the linear programming problem. This means that there are no feasible solutions in the feasible region. If the initial basic feasible solution is infeasible, then the simplex method cannot be used to obtain a feasible solution.

2. Unbounded solution: An unbounded solution is a solution that does not have an optimal value because the objective function can be made arbitrarily large or small. This occurs when the feasible region is unbounded in the direction of the objective function. In this case, the simplex method cannot be used to find the optimal solution.

3. Degenerate solution: A degenerate solution is a solution where one or more of the variables take on a value of zero. This causes the simplex method to get stuck in a loop, which can slow down the convergence to the optimal solution. However, the simplex method can still find the optimal solution for degenerate problems.

4. Multiple optimal solutions: Multiple optimal solutions are solutions that have the same optimal value. This occurs when the objective function is parallel to one or more of the constraints, and the feasible region is unbounded in that direction. In this case, the simplex method can find any one of the optimal solutions, but cannot identify all of them.

Therefore, the correct answer is option B, infeasible solution, as the simplex method cannot find a solution that violates the constraints of the linear programming problem.