Consider the following linear program.

Max $3A+2B$

$s.t.$

$q,1A+1B10$

$,3A+1B27$

$,1A+2B20$

$,A,B0$

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?

$($b$)$ Use the solution to part $($a$)$ to determine the dual value for constraint $1.$

$($c$)$ The computer solution for the linear program provides the following right$-$hand side range information.

What does the right$-$hand side range information for constraint $1$ tell you about the dual value for constraint $1?$

The range for constraint $1$ is

tc

$.$ As long as the right$-$hand side stays

$--$ Select$--$

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$-$hand 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 long as the right$-$hand side is

the

range

to