Considering the following LP problem:

MaxZ$=,5x_1+12x_2$

$s.t.x_1+x_{2}25$

$,3x_1+x_{2}45$

$,5x_1+7x_{2}20$

$,7x_1+13x_{2}83$

$,x_1,x_{2}0$

Which one of the following options is correct?

The problem is infeasible

The problem is unbounded

There is more than one optimal solution

$(12,7)$ is the optimal solution

None of the above