Question $3$

Consider the LP shown below.

max,$5x_1+x_2+7x_3$

$s.t.x_1+x_2+2x_3=17$

$,x_1+3x_{2}12$

$,4x_1+x_2+x_{3}20$

$,5x_2+x_{3}56$

$,x_1,x_2,x_{3}0$

a$)$ Construct the LP in standard form.

b$)$ Construct the phase$-1$ artificial LP$.$

c$)$ Find the optimal tableau at the end of phase$-1.$

d$)$ Construct the initial tableau of phase$-2.$ State the entering and leaving variables.

e$)$ Construct the big$-$M artificial LP$.$

f$)$ Construct the proper simplex tableau to start applying the big$-$M method. State the entering

and leaving variables.