Consider the following linear program:

max

x z $=4$x$1+4$x$2+6$x$3$

s$.$t$.2$x$1+2$x$2+$x

x$1+2$x$2$x

x$1,$ x$2,$ x$3>=0.$

A$)$ Write down the dual of this linear program.

B$)$ Solve the dual LP using the graphical method.

C$)$ Use complimentary slackness to construct the optimal solution of the primal problem.

Question $2.(30$ points$)$: Consider the following linear program:

$ma{x}_x,z=,4x_1+4x_2+6x_3$

$s.t.2x_1+2x_2+x_{3}4,$

$,x_1+2x_2-x_{3}9,$

$,x_1,x_2,x_{3}0.$

A$)$ Write down the dual of this linear program.

B$)$ Solve the dual LP using the graphical method.

C$)$ Use complimentary slackness to construct the optimal solution of the primal problem.