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$3<=4,$

x$1+2$x$2$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