*3. Consider the following LP:

Maximize z = 5Xl + 2X2 + 3X3 subject to Xl + 5X2 + 2X3 = 30 Xl - 5X2 - 6X3 S; 40 Given that the artificial variable X4 and the slack variable X5 form the starting basic variables and that M was set equal to 100 when solving the problem, the optimal tableau is given as Basic z o 1o Xz 23 5

-10 7

2

-8 105 1

-1 o

o 1

Solution 150 30 10 I

Write the associated dual problem and determine its optimal solution in two ways.

.. ,j i.~·.·.. ·.. .' :_...

4.2 Primal-Dual Relationships 163