Exercise #$3$

Consider the following LP:

max,$Z=x_1+2x_2$

subject $to{x}_1-x_{2}1$

$,2x_1+3x_{2}3$

$,x_1,x_{2}0$

Show that the problem is unbounded.

Show that the dual problem of the LP above can be written as:

min,$W=y_1-3y_2$

subject $to{y}_1-2y_{2}1$

$,-y_1-3y_{2}2$

$,y_1,y_{2}0$

Show that the dual is now infeasible.

Briefly explain why the result from point $(3)$ was expected as soon as we realized that the primal problem was unbounded, without even having to write the dual.