$*3-18.$ Consider the three$-$dimensional LP solution space in Figure $3\mathrm{.}17$ whose feasible

extreme points are $A,B,$dots, and $J.$

Figure $3\mathrm{.}17$

Solution space of Problem $3-18$

$($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 is not legitimate

for the simplex algorithm, and state the reason.

$($i$)ABGH.$

$($ii$)AEIH.$

$($iii$)ACEBADGH.$