$(20$ pts$)$ Use the dual simplex method manually to solve the following

Minimize $,Z=7x_1+2x_2+5x_3+4x_4,$

subject to

$2x_1+4x_2+7x_3+x_{4}5$

$8x_1+4x_2+6x_3+4x_{4}8$

$3x_1+8x_2+x_3+4x_{4}4$

and

$x_{j}0,$ for $j=1,2,3,4.$