Q$1.$ Consider the following linear model:

maxZ$=2x_1+8x_2+x_3$

$s.t.2x_1+4x_{2}12$

$2x_1+2x_2+x_{3}4$

$x_1,x_{2}0$

$($a$)$ What is the Basic Feasible Solution with basic variables $(x_1,s_1)?$

$($b$)$ Solve above LP with Simplex Method.