Suppose that either Phase I is completed or the bounded optimal solution of the big-M problem is found. Furthermore, suppose that there is exists at least one artificial at a positive level indicating that the original system Ax=b and x>=0 has no solution. How would you differentiate between the following two cases?

a. The system Ax=b is inconsistent.

b. The system Ax=b is consistent but Ax=b implies that x~>=0. Illustrate each case with an example.