Consider the following linear program.

Max	3A	+	2B
s.t.
	1A	+	1B		10
	3A	+	1B		26
	1A	+	2B		18
	A,	B	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 (A, B) =

(b)

Assume that the objective function coefficient for A changes from 3 to 5. Use the graphical solution procedure to find the new optimal solution.

Does the optimal solution change?

The extreme point

---Select--- remains becomes optimal. The value of the objective function becomes .

(c)

Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 4. Use the graphical solution procedure to find the new optimal solution.

Does the optimal solution change?

The extreme point

---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
A	3.00000	3.00000	1.00000
B	2.00000	1.00000	1.00000

Use this objective coefficient range information to answer parts (b) and (c).

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