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.