$3-12.$ Determine the optimum solution for each of the following LPs by enumerating all the basic solutions.

$($a$)$ Maximize $z=2x_1-4x_2+5x_3-6x_4$ subject to

$x_1+4x_2-2x_3+8x_{4}2$

$-x_1+2x_2+3x_3+4x_{4}1$

$x_1,x_2,x_3,x_{4}0$

$($b$)$ Minimize $z=x_1+2x_2-3x_3-2x_4$ subject to

$x_1+2x_2-3x_3+x_4=4$

$x_1+2x_2+x_3+2x_4=4$

$x_1,x_2,x_3,x_{4}0$