4. Consider the following LP:

Minimize z = 4x, + X2 subject to 3Xl + X2 = 3 4X1 + 3X2 ;::: 6 XI + 2X2 :0:; 4 The starting solution consists of artificial X4 and Xs for the first and second constraints and slack X6 for the third constraint. Using M = 100 for the artificial variables, the optimal tableau is given as Basic XI X2 X3 X4 Xs x6 Solution z 0 0 0 -98.6 -100 -.2 3.4 XI 1 0 0 .4 0 -.2 .4 Xl 0 1 0 .2 0 .6 1.8 x3 0 0 1 1 -1 1 1.0 Write the associated dual problem and determine its optimal solution in two ways.