Consider the following linear program.

Min	8X	+	12Y
s.t.
	1X	+	3Y		9
	2X	+	2Y		14
	6X	+	2Y		18
	X,	Y	0

(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) =

(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 (X, Y) =

---Select--- remains 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.

Does the optimal solution change?

The extreme point (X, Y) =

---Select--- remains becomes 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.

Variable	Objective Coefficient	Allowable Increase	Allowable Decrease
X	8.00000	4.00000	4.00000
Y	12.00000	12.00000	4.00000

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 ---Select--- within outside this range, we know the optimal solution ---Select--- will will not change. The objective coefficient range for variable Y is to . Since the change in part (c) is ---Select--- within outside this range, we know the optimal solution ---Select--- will will not change.