$(1).$ Consider the LP below. The BFS $($corners$)$ are $(0,0)(0,4)(4/3,10/3)(3,0).$ The optimal solution is at x$1=4/3$ and x$2=10/3.(1).$ Consider the LP below. The BFS $("$corners$")$ are $(0,0)(0,4)(\frac{4}{3},\frac{10}{3})(3,0).$ The optimal solution is at

$x_1=\frac{4}{3}$ and $x_2=\frac{10}{3}.$

max,$z=x_1+x_2,$

$s.t.x_1+2x_2,8$

$,2x_1+x_2,6$

$,x_1,x_2,0$

$($a$).$ What is the range of $c_1$ the objective coefficient of $x_1($currently $1)$ for which this BFS remains optimal:

$($b$).$ What is the range of $b_2,$ the right hand side of the second constraint $($currently $6)$ for which this BFS

remains optimal?

max z$=$x$1+$x$2$

s$.$t$.$ x$1+2$x

$2$x$1+$ x x$1,$x$2>=0$

$($a$).$ What is the range of c$1$ the objective coefficient of x$1($currently $1)$ for which this BFS remains optimal: $($b$).$ What is the range of b$2,$ the right hand side of the second constraint $($currently $6)$ for which this BFS remains optimal