$z=30$ min $*10$ total points

Consider the LPP given below.

Maximize $z=-4x_1-2x_2-3x_3-x_4$

such that,

$x_1+4x_2+2x_{3}8$

$4x_1+2x_2-7x_{3}7$

$2x_1-4x_{4}2$

$2x_2+2x_4-1$

$x_1,x_2,x_3,x_{4}0$

After ensuring that all the conditions for using the dual simplex method are met and adding the necessary

slack$/$surplus variables, what does the problem look like?

Dual simplex method cannot be used to obtain the solution to this problem despite making modifications.

Maximize $z=-4x_1-2x_2-3x_3-x_4$

such that,

$-x_1-4x_2-2x_3+s_1=8$

$4x_1+2x_2-7x_3+s_2=-7$

$-2x_1+4x_4+s_3=2$

$-2x_2-2x_4+s_4=-1$

$x_1,x_2,x_3,x_4,s_1,s_2,s_3,s_{4}0$

Maximize $z=-4x_1-2x_2-3x_3-x_4$

such that,

$-x_1-4x_2-2x_3+s_1=-8$