Write the dual from the following linear programming model:

Max Z $=3$ X$1+2$ X$2+5$ X$3$

S$.$TO:

X$1+2$ X$2+$ X$3<=430$

$3$X$1+2$X$3<=460$

X$1+4$X$2<=420$

X$1,$X$2,$X$3>=0$