$4-$ For the two models below, provide the standard for of the linear programs, i$.$e$.,$ in the form mincx s$.$t$.$ Ax$=$b $,x0.$ Also provide insights about how you would find an initial basic feasible solution for the models in order to start the Simplex method.

Consider the following linear programs:

$mi{n}_x,5x_1+x_2-4x_3$

$s.t.x_1+x_2+x_3+x_4,19$

$,$

$4x_2,+8x_4,55$

$,x_1+6x_2-x_3,=7$

$,x_1$ unrestricted, $x_{2}0,x_{3}0,x_{4}0$

and

$ma{x}_x,2x_1-7x_2+6x_3+5x_4$

$s.t.2x_1-3x_2-5x_3-4x_{4}20$

$,7x_1+2x_2+6x_3-2x_4=35$

$,4x_1+5x_2-3x_3-2x_{4}15$

$,0x_{1}10,0x_{2}5,x_{3}2,x_{4}0$