$(25$ pts$.)$ Find the optimal solution for the following LP problem using the appropriate simplex method.

$($Hint: DO NOT use the big$-M$ method$)$

Minimize $Z=5x_1+2x_2+4x_3$

$s.t.3x_1+x_2+2x_{3}4$

$6x_1+3x_2+5x_{3}10$

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

and