$4-17.$ Estimate a range for the optimal objective value for the following LPs:

$*($a$)$ Minimize $z=5x_1+2x_2$ subject to

$x_1-x_{2}3$

$2x_1+3x_{2}5$

$x_1,x_{2}0$

$($b$)$ Maximize $z=x_1+5x_2+3x_3$ subject to

$x_1+2x_2+x_3=30$

$2x_1-x_2=40$

$x_1,x_2,x_{3}0$

Utilize weak duality theorem