Consider the linear program:

max $20$x$1+10$x$2$

s$.$t$.40$x$1+30$x$2>=120$

$$x$1+$ x$2<=1$

x$1<=3$

x$1,$ x$2>=0$

$($a$)$ Formulate the linear program in standard form.

$($b$)$ Solve the linear program using the simplex method.

$($c$)$ Solve the linear program graphically.

$($d$)$ Show the iterations of the simplex method on the figure