Problem $3-02($Algorithmic$)$

Consider the following linear program:

Max $3A+2B$

$s.t.$

$,1A+1B8$

$,3A+1B21$

$,1A+2B16$

$A,B0$

The value of the optimal solution is $22\mathrm{.}5.$ Suppose that the right$-$hand side of the constraint $1$ is increased from $8$ to $9.$