Max $z = -2x_1 – x_3 \\ \space s.t. \space x_1 + x_2 – x_3 ≥ 5\\ x_1 -2x_2+ 4x_3 ≥ 8 \\ \space\&\space x_1, x_2, x_3 ≥ 0 $

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 08

Year : MAY 2014

In dual simplex we write the objective function as maximization type and constraints in “≤” type

Objective:

Maximize $z=-2x_1+0x_2-1x_3;$

Constraints: Multiplying each constraints by “-1”

$i) -1x_1-1x_2+1x_3 ≤ 5 \\ ii) -1x_2+2x_2-4x_3 ≤ -8;$

Converting each constraint into equality by adding slack variable,

Maximize $z=-2x_1+0x_2-1x_3+0s_1+0s_2;$

Constraints

$-1x_1-1x_2+1x_3+1s_1+0s_2=-5; \\ -1x_1+2x_2-4x_3+0s_1+1s_2=-8; \\ x_1,x_2,x_3,s_1,s_2 ≥ 0$

For maximization $X_1=0; X_2=14; X_3=9; Z_{max}=-9$