Given the following all$-$integer linear programming problem:

Max $3x_1+4x_2$

$s.t.5x_1+x_{2}100$

$4x_1+2x_{2}75$

$3x_1-x_{2}0$

$2x_1+3x_{2}0$

$,x_1+4x_{2}0$

$x_1,x_{2}0$ and integer