Consider the following linear program.

Min $8x+12Y$

$s.t.$

$1x+3Y8$

$2x+2Y12$

$6x+2Y16$

$x,Y0$

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

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

$at(x,n)=(,)$

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

The extreme point

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$[[$Variable$,$Objective,Allowable,Allowable$]]$