For the linear program of Exercise $4$ in $2024-$AOR$-$HW$2$

$($a$)$ How much can the elements of $b=(4,3,3)$ be changed without changing the optimal

basis?

$($b$)$ How much can the elements of $c=(2,4,1,1)$ be changed without changing the

optimal basis?

$($c$)$ What happens to the optimal cost for small changes in $b?$

$($d$)$ What happens to the optimal cost for small changes in $c?$