*3. Consider the three-dimensional LP solution space in Figure 3.4, whose feasible extreme points are A, B, ... , and 1.

(a) Which of the following pairs of corner points cannot represent successive simplex iterations:

(A, B), (B, D), (E, H), and (A, I)? Explain the reason.

(b) Suppose that the simplex iterations start at A and that the optimum occurs at H. Indicate whether any of the following paths are not legitimate for the simplex algorithm, and state the reason.

(i) A-B-G-H.

(ii) A-E-I-H.

(iii) A-C-E-B-A-D-G-H.