$(1).$ 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$2=10/3.$

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

s$.$t$.$ x$1+2$x$2<=8$

$2$x$1+$ 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