Consider the following all$-$integer linear program.

Max $1x_1+1x_2$

$s.t.$

$,5x_1+6x_{2}41$

$,1x_1+5x_{2}20$

$,2x_1+1x_{2}15$

$x_1,x_{2}0$ and integer

$($a$)$ Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.

$($i$)$

$($i$)$

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

$at(x_1,x_2)=1$

$($c$)$ Find the optimal integer solution.

$at(x_1,x_2)=(,)$