Primal: Maximize z = c^{t}X subject to A X < = b, X > = 0.
Maximize z = 30 x_{1} + 6 x_{2}  5 x_{3} + 18 x_{4}
 Dual: Minimize w = b^{t}Y subject to A^{t} Y > = c, Y > = 0.
Minimize w = 20 y_{1} + 15 y_{2}+ 54 y_{3}


 
Inititial Tableau  Final Tableau 
Step 1
[ 
1 0 2 1 2 1 0 1 6 2 3 0  ]  [  0 27 0 20  ]  = [  20 7 54  ]  < [  20 15 54  ] 
Step 2
Since x_{2}^{*} = 27 and x_{4}^{*} = 20, we conclude that the inequalities in the second and forth rows of the dual system must be equalities. By replacing y_{2} with zero in
{  y_{2} + 2 y_{3} = 6 y_{1}  y_{2} = 18 