Q$4$: Consider the following linear program:

$z^{**}=$min,$4x_1+3x_2-7x_3+3x_4,$

$s.t.5x_1+3x_2-5x_4,21$

$,x_1+4x_2-12x_3,=17$

$,x_2-4x_3+2x_4,5$

$,x_1,x_2,x_3,x_4,0$

$($a$)$ What would $A,b$ and $c$ be if you write this LP in the following $$ form:

$min{c}^{T}xs.t.Axb,x0$

$($b$)$ What would $A,b$ and $c$ be if you write this LP in the following $$ form:

$min{c}^{T}xs.t.Axb,x0$

$($c$)$ Same question, but this time write the LP in equality form $($using additional variables$).$

$($d$)$ Can you write a linear program with a maximization objective that would find the optimal solution to the problem above $($which originally has a minimization objective$)?$