Consider the following linear program.

$[$ Max $3$ A$+2$ B; s$.$t$.$; $1$ A$+1$ B $<=10$; $3$ A$+1$ B $<=27$; $1$ A$+2$ B $<=20$; A$,$ B $>=0]$

The value of the optimal solution is $28\mathrm{.}5.$ Suppose that the right$-$hand side for constraint $1$ is increased from $10$ to $11.($a$)$ Use the graphical solution procedure to find the new optimal solution. What is the value of the objective function at the optimal solution?

at $($A$,$ B$)=($

$($b$)$ Use the solution to part $($a$)$ to determine the dual value for constraint $1.($c$)$ The computer solutien for the Inear program provides the follewing right$-$hand side range information. What does the right$-$hand side range information for constraint $1$ teil you about the dual value for constraint $1?$ The range for constraint $1$ is to As long as the right$-$hand side stays this range, the dual value of is applicable, $($d$)$ The dual value for constraint $2$ is $0\mathrm{.}5.$ Using this dual value and the right$-$hand side range information in part $($c$),$ what conclusion can be drawn about the effect of changes to the right$-$hant side of constraint $2?$ The value of the optimal solution will increase by for every unit increase in the right$-$hand side of constraint $2$ as lang as the right$-$hand side is the range to