$3-38.$ Consider the following set of constraints:

$x_1+x_2+x_3=7$

$2x_1-5x_2+x_{3}10$

$x_1,x_2,x_{3}0$

Solve the problem for each of the following objective functions:

$($a$)$ Maximize $z=2x_1+3x_2-5x_3.$

$($b$)$ Minimize $z=2x_1+3x_2-5x_3.$

$($c$)$ Maximize $z=x_1+2x_2+x_3.$

$($d$)$ Minimize $z=4x_1-8x_2+3x_3.$