State the dual problem for the following, but do not solve it$.$

Minimize $w=y_1+5y_2+6y_3+7y_4$

Subject to:

$3y_1+6y_2+7y_3+y_4-4$

$y_1+6y_2+6y_3+y_{4}10$

$y_{1}0,y_{2}0,y_{3}0,y_{4}0$

Maximize $z=,x_1+10x_2$

Subject $to$:

$1$

$5$

$6$

$7$

$x_{1}0,x_{2}0$