Consider the three-dimensional LP solution space in Figure 3.16, whose feasible extreme points are A, B, . . . , and J.

(a) Which of the following pairs of corner points cannot represent successive simplex iterations: (A, B), (H, I ), (E, H ), and (A, I )? Explain why.

(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) AS B S GS H.

(ii) AS DS F S C S AS B S GS H.

(iii) AS C S I S H.