Q$3$ Solve the following LP problem graphically by enumerating the corner points.

max $8$X$1+12$ X$2$

$6$X$1+4$ X$2<=24$

X$1+2$ X$2<=6$

$-$X$1+$ X$2<=3$

X$2<=2$

X$1,$ X$2>=0$

$1.$ Plot the constraints of the problem. Show the feasible area.

$2.$ Which constraint is the redundant constraint.

$3.$ List the feasible corner points

$4.$ Calculate the objective function at each feasible corner points

$5.$ Which point is the optimal point?

$6.$ Which constraint are binding at the optimal point?

$7.$ Determine the range of $$ in the objective function $(8+)$x$1+12$x$2$ that the current solution is the optimal solution. Show the details.