answer for all the boxes please.

Consider the following linear program.

Max$3A+2B$

$s.t.$

$1A+1B10$

$3A+1B26$

$1A+2B18$

$A,B0$

$($a$)$ Use the graphical solution procedure to find the optimal solution.

What is the value of the objective function at the optimal solution?

$($b$)$ Assume that the objective function coefficient for A changes from $3$ to $5.$ Use the graphical solution procedure to find the new optimal solution.

Does the optimal solution change?

The extreme point $()--$Select$--$v optimal. The value of the objective function becomes

Does the optimal solution change?

The extreme point

$-$Select$-$

optimal. The value of the objective function becomes

$.$

$($c$)$ Assume that the objective function coefficient for A remains $3,$ but the objective function coefficient for $B$ changes from $2$ to $4.$ Use the graphical solution procedure to find the new optimal solution.

Does the optimal solution change?

The extreme point

Select$-v$

optimal. The value of the objective function becomes

$($d$)$ The computer solution for the linear program in part $($a$)$ provides the following objective coefficient range information.

Use this objective coefficient range information to answer parts $($b$)$ and $($c$).$

The objective coefficient range for variable $A$ is

to

$.$ Since the change in part $($b$)$ is

$|$ this range, we know the optimal solution

Select$-$

change. The objective

coefficient range for variable $B$ is

to

$.$ Since the change in part $($c$)$ is $-$ Select$-$ this range, we know the optimal solution

change.

Consider the following linear program.

$($c$)$ Assume that the objective function coefficient for A remains $3,$ but the objective function coefficient for $B$ changes from $2$ to $4.$ Use the graphical solution procedure to find the new optimal solution.

Does the optimal solution change?

The extreme point

Select$-$

optimal. The value of the objective function becomes

$].$

$($d$)$ The computer solution for the linear program in part $($a$)$ provides the following objective coefficient range information.

Use this objective coefficient range information to answer parts $($b$)$ and $($c$).$

The objective coefficient range for variable $A$ is

to $$

Since the change in part $($b$)$ is

this range, we know the optimal solution

Select$-v$

change. The objective

coefficient range for variable $B$ is

to

Since the change in part $($c$)$ is

$-$Select$-$

this range, we know the optimal solution

change.

Consider the following linear program.