Consider the following linear program.

Max $3$A $+2$B

s$.$t$.$

$1$A $+1$B $<=10$

$3$A $+1$B $<=24$

$1$A $+2$B $<=20$

A$,$ B $>=0$

The value of the optimal solution is $27\mathrm{.}0.$ Suppose that the right$-$hand side for constraint $1$ is increased from $10$ to $11.$

$($a$)$