$4$

$.$

$3$

$.$

$$Solve the problem

minimize z

$=$

$$

$4$

x

$1$

$$

$2$

x

$2$

subject to

$3$

x

$1$

$$

$2$

x

$2$

$>$

$=$

$4$

$$

$2$

x

$1$

$+$

$$x

$2$

$=$

$2$

x

$1$

$,$

$$x

$2$

$,$

$>$

$=$

$0$

$,$

using

$($

a

$)$

$$the two

$-$

phase method;

$($

b

$)$

$$the big

$-$

M method