Consider the following linear program.

Min	8X	+	12Y
s.t.
	1X	+	3Y		7
	2X	+	2Y		10
	6X	+	2Y		14
	X,	Y	0

A. Use the graphical solution procedure to find the optimal solution. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution.)

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

_______ at (X,Y)= ( ______)

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. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution.)

Does the optimal solution change?

The extreme point (_______) ***remains or becomes*** 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 solution procedure to find the new optimal solution. (Graph the constraint lines, the feasible region, the objective function line, and the optimal solution.)

Does the optimal solution change?

The extreme point (_______) ***remains or becomes*** optimal. The value of the objective function becomes ______.