Problem $1$

Use branch and bound method to find the optimal solution of the following integer programming

problem. Use graphical method to solve the linear programming sub$-$problems.

Maxz$=x_1+2x_2$

St$.$

$x_1+x_{2}5$

$x_1-x_{2}0$

$2x_1+6x_{2}21$

$x_{1}0,x_{2}0$

$x_1,x_2$: integer