Consider the following LP:

Maximize z = 5x1 + 12x2 + 4x3 subject to 2x1 - x2 + 3x3 = 2 x1 + 2x2 + x3 + x4 = 5 x1, x2, x3, x4 Ú 0

(a) Write the dual.

(b) In each of the following cases, first verify that the given basis B is feasible for the primal. Next, using Y = CBB-1, compute the associated dual values and verify whether or not the primal solution is optimal.

(i) B = 1p4, p32

(ii) B = 1p2, p32

(iii) B = 1p1, p22

(iv) B = 1p1, p42