Max $3A+2B$

$s.t.$

$1A+1B10$

$3A+1B27$

$1A+2B20$

$A,B0$

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. $($Graph the constraint lines, the feasible region, the objective function line,

and the optimal solution.$)$

Graph Layers

After you add an object to the graph you

can use Graph Layers to view and edit its

properties.

$($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

$($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