Question

Solve this problem using the two-phase method. What special case do you observe? Max Zz4X1-2X2+X3 X1+2X2+X3 3 2X1-3X2+6X3 100 X1,X2,X3>0

Answer 1

Z = x_1 - 2x_2 + x_3 x_1 + 2x_2 + x_3 > = 3 2x_1 - 3x_2 + 6x_2 < = 100 x_1, x_ 2, x_3 > = 0 Adding slack, surplus artificial variables. Max z = -A_1 subject to. X_1 + 2x_2 + x_3 - s_1 + A_1 = 3 2x_1 - 3x_2 + 6x_2 + s_2 = 100 x_1, x_2, x_3, s_1, s_2, A_1 lessthanorequalto 0 z_j - g -2 column index is 2 entering row x_2 min ratio 1.5 row index is 1 base variable A_1 R_1(new) = R_1(odd) 2 R_2(new) = R_2(old) + 3R_1(new) all z_j - c_j lessthanorequalto 0. Optimal solution is arrived. X_1 = 0, x_2 3/2, x_3 = 0, max z = 0. In phase we elimination the artificial variables & change the objective function for the original. Z_j - c_j = -4 (neg) entering value s, _1 min ratio 47 & row index 2 leaving