Consider the following linear programming problem max z

$=$

$4$

$0$

x

$1$

$+$

$5$

$0$

x

$2$

$$s

$.$

t

$.$

x

$1$

$+$

$2$

x

$2$

$<$

$=$

$4$

$0$

$$x

$1$

$+$

$$x

$2$

$<$

$=$

$3$

$0$

$2$

x

$1$

$+$

$$x

$2$

$<$

$=$

$4$

$0$

$$x

$1$

$,$

x

$2$

$>$

$=$

$0$

$$An optimal tableau for this LP is shown in the following table. z x

$1$

$$x

$2$

$$s

$1$

$$s

$2$

$$s

$3$

$$rhs

$1$

$0$

$0$

$2$

$0$

$0$

$1$

$0$

$1$

$2$

$0$

$0$

$0$

$0$

$1$

$2$

$/$

$3$

$0$

$-$

$1$

$/$

$3$

$4$

$0$

$/$

$3$

$0$

$0$

$0$

$-$

$1$

$/$

$3$

$1$

$-$

$1$

$/$

$3$

$1$

$0$

$/$

$3$

$0$

$1$

$0$

$-$

$1$

$/$

$3$

$0$

$2$

$/$

$3$

$4$

$0$

$/$

$3$

$$Find the range of values of c

$1$

$($

coefficient of x

$1$

$$in objective function

$)$

$$for which the current basis remains optimal.