Optimum Structural Design

Linear programming problem using graphical and Algebric methods

Minimize $f=2x_1+x_2$

Subject to$$

$g_1=4x_{2}1$

$g_2=2x_1+2x_{2}1$

$g_3=x_1+x_{2}1$

$g_4=2x_{1}1$

$g_5=2x_1+4x_{2}3$

$g_6=4x_1+2x_{2}3,x_{1}0$ and $x_{2}0$ Please solve it in handwriting and in$$detail