Given the following all$-$integer linear program:

Max $3x_1+2x_2$

$s.t.3x_1+x_{2}9$

$x_1+3x_2,7$

$-x_1+x_2,1$

$x_1,x_2,0$ and integer

Solve the problem as a linear program ignoring the integer constraints. Show that the optimal solution to the linear program gives fractional values for both $x_1$ and $x_2.$