Consider the following all$-$integer linear program:

Max,$x_1+x_2$

$s.t.$

$,4x_1+6x_{2}22$

$,x_1+5x_{2}15$

$,2x_1+x_{2}9$

$,x_1,x_{2}0$ and integer

a$.$ Choose the correct graph which shows the constraints for this problem and uses dots to indicate all feasible integer solutions.

$($i$)$

$($ii$)$

$($iii$)$

$($iv$)$

b$.$ Solve the LP Relaxation of this problem.

The optimal solution to the LP Relaxation is $x_1=$

$,x_2=$

Its value is

c$.$ Find the optimal integer solution.

The optimal solution to the LP Relaxation is $x_1=$

$,x_2=$

Its value is