Working with the Lagrangian Dual problem.

Hello, Could you please help me to prove this using Farkas Lemma? Well, I initially thought that I can use Farkas Lemma, but if it is impossible to use the lemma (though I do belive it will help), you might try other way.

Considering the following linear programming problem: max -2x + y -z -3x + y -2z <= 10 -x - y -2z <= 5 x,y,z >= 0 (legend: <= means less than equal and >= means greater than equal) a) Form the dual linear programming problem b) Solve the dual geometrically Draw the lines -3p - q = -2, p - q = 1, -2p - 2q = -1 on the same (p,q) axes c) Determine the min of the dual problem: ___ and where it occurs: (p,q)=____ c) Determine the max of the primal problem: ___ and where it occurs: (x,y,z)=____.