Could you please help me solve the problem shown in the image? I would greatly appreciate it if you could provide a detailed, step$-$by$-$step solution and write MATLAB code.

$(20$ pts$)$ Consider the integer linear program:

min,$16x_1+14x_2+15x_3$

$s.t.x_1+x_{2}1$

$,x_2+x_{3}1$

$,x_3+x_{1}1$

$,x_1,x_2,x_{3}in\{0,1\}.$

$($a$)$ Find the optimal solution by inspection or enumeration.

$($b$)$ Show that an equivalent integer linear program would result if the main constraints $(2)-(4)$ were replaced by

$x_1+x_2+x_{3}2$

i$.$e$.,$ that the feasible sets of the two problems are identical.

$($c$)$ Compare the optimal solutions of the linear programming relaxation of the two formulations. Discuss what you observe and which formulation is better. You can use CVX to solve the linear programming relaxation problems.