5. Consider the following LP model:

Maximize z = 5XI + 12x2 + 4x~

subject to Xl + 2X2 + X3 + X4 == 10 2XI - X2 + 3X3 == 2

(a) Identify the best solution from among the following basic feasible solutions:

(

(i) Basic variables = (X4. X3), Inverse = 01 --3il)

(~ ---~~) (ii) Basic variables = (X2, Xl)' Inverse = i

(

(iii) Basic variables = (X2, X3), Inverse = ~;! -77-21_)

(b) Is the solution obtained in

(a) optimum for the LP model?