2. Consider the following LP model:

Maximize z = 4x) + 14x2 subject to 2x] + txz + X3 = 21 7x) + 2X2 + X4 = 21 xl> x2, x3' X4 ~ 0 4.2 Primal-Dual Relationships 167 Check the optimality and feasibility of each of the following basic solutions.

*

(a) Basic variables = (X2, X4), Inverse = (_~ ~)

7

(b) Basic variables = (X2' X3), Inverse = (~ j)

2 7 2

(c) Basic variables = (X2, xd, Inverse = (_~ -~)

45 45

)

(d) Basic variables = (x), X4), Inverse = (_~ ~)

2