$(1).$ 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?