$3.$ Consider the following linear program:

$[$ Min $8$ X$+12$ Y; s$.$t$.$ ; $1$ X$+3$ Y $>=9$; $2$ X$+2$ Y $>=10$; $6$ X$+2$ Y $>=18$; A$,$ B $>=0]$

a$.$ Use the graphical solution procedure to find the optimal solution. b$.$ Assume that the objective function coefficient for X changes fror. $8$ to $6.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. c$.$ Assume that the objective function coefficient for X remains $8,$ but the objective function coefficient for Y changes from $12$ to $6.$ Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. d$.$ The computer solution for the linear program in part $($a$)$ provides the following objective coefficient range information: