4. For the solution space in Figure 3.4, all the constraints are of the type :5 and all the variables XI> X2, and X3 are nonnegative. Suppose that SJ, S2, s3, and S4 (~ 0) are the slacks associated with constraints represented by the planes CEllF, BEIHG, DFJHG, and IIH, respectively. Identify the basic and nonbasic variables associated with each feasible extreme point of the solution space.

FIGURE 3.4 Solution space of Problem 3, Set 3.2b G

)------"

3.:

F t-----

-}---Xj A: (0,0,0)

B: (1,0,0)

C: (0, 1,0)

D: (0,0,1)

3.3 The Simplex Method 93