Consider the following linear program.

$]7[0$

$($a$)$ Use the graphical solution procedure to find the optimal solution. What is the value of the objective function at the optimal selution?

$at(x,n)=\{15,36\}$

$($b$)$ Assume that the objective function coefficient for $x$ changes from $8$ to $6.$ Use the graphical solution hecedure to find the new optimal solution. Does the optimal solution change?

The extreme point $-$Select$-$y optimal. The value of the objective function becomes

$($C$)$ Assume that the objective function coefficient for X remains $8,$ but the objective function coefficient for Y changes from $12$ to $6.$ Use the graphical solutio Does the optimal solution change? The extreme point $-$Select$-$y 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.

$\backslash$table$[[$Vartable$,\backslash$table$[[$Objective$],[$Coefincient$]],\backslash$table$[[$Milowable$],[$Increase$]],\backslash$table$[[$Allowable$],[$Decrease$]]],[x,8\mathrm{.}00000,4\mathrm{.}00000,4\mathrm{.}00000],[r,12\mathrm{.}00000,12\mathrm{.}00000,4\mathrm{.}00000]]$

How would this objective coefficient range information help you answer parts $($b$)$ and $($c$)$ prior to re$-$solving the problem?

The objective coefficient range for variable $x$ is

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