$[25$ pts$.]$ Use the Simplex and Big M Method to find the optimum solution to the following LP$.$ Write standard form and use simplex table format. $($Write the simplex table for each iteration and show the calculations$)$

minz$=,4x_1+4x_2+x_3$

$s.t.x_1+x_2+x_{3}2$

$2x_1+x_{2}3$

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

$,x_1,x_2,x_3^{3}0$