Consider the following linear program.

Min $8x+12Y$

$s.t.$

$1x+3Y6$

$2x+2Y8$

$6x+2Y12$

$x,Y0$

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

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

$at(x,y)=,x$

$($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 $($I$)$