PRIMAL$-$DUAL CONVERSION

$3.$ Convert the following problems into their dual

$($a$)$ Maximize

$($b$)$ Minimize

$z=66x_1-22x_2,z=6x_1+3x_2$

Subject to

Subject to

$-x_1+x_2-2$

$2x_1+3x_{2}5$

$x_1,x_{2}0$

$6x_1-3x_2+x_{3}25$

$3x_1+4x_2+x_{3}55$

$x_1$ unrestricted

$x_2,x_{3}0$