Consider the following mixed$-$integer linear programming problem

max z$=7$x$1+2$x$2$

s$.$t$.$

$$x$1+2$x$24$

$2$x$1+$x$25$

x$1+2$x$22$

x$22$

x$10,$ x$2$ integer

a$.$Show graphically the feasible solution set.

b$.$Solve the problem $($determine an optimum solution and optimal value$)$ graphically. c$.$Show graphically the convex hull of the feasible solution set.

d$.$Give the algebraic description of the convex hull.

e$.$Solve graphically the LP consisting of the maximization of the objective function subject to the constraints describing the convex hull. What do you observe?