Write the dual for each of the following primal problems:

Maximize $u=-5x_1+2x_2$

Subject to:

$-x_1+x_2-2$

$2x_1+3x_{2}5$

$x_1,x_{2}0$

Maximize $u=-x_1+2x_2-3x_3$

Subject to:

$x_1-x_2-2$

$2x_1+x_2-x_{3}15$

$x_2+x_3=10$

$x_1,x_{2}0$

$x_3$ unrestricted

Minimize $z=6x_1+3x_2$

Subject to:

$6x_1-3x_2+x_{3}2$

$3x_1+4x_2+x_{3}5$

$x_1,x_2,x_{3}0$