Consider the following linear program.

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 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

to

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

this range, the dual value of

is applicable.

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