Problem 3-01 (Algorithmic)

Consider the following linear program:

Max	3A + 2B
s.t.
	1A + 1B 14
	3A + 1B 26
	1A + 2B 16
	A, B 0

B. Assume that the objective function coefficient for A changes from 3 to 4. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution

_____________ (The same extreme point remains optimal or a new extreme point becomes optimal)

If required, round your answers to one decimal place.

A
B
Optimal solution

C. Assume that the objective function coefficient for A remains 3, but the objective function coefficient for B changes from 2 to 7. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution.

_________________(Same options as step B)

If required, round your answers to one decimal place.

A
B
Optimal solution

D. The sensitivity report 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		2.00000
		B		2.00000		4.00000		1.00000

Use this objective coefficient range information to answer parts (b) and (c). The objective coefficient range for A is from __________ to _________ so the optimal solution ______ change in part (b) because the new objective coefficient is ________ this range. The objective coefficient range for B is from ________ to fill ___________ so the optimal solution _______ change in part (c) because the new objective coefficient is _____this range.

a. Choose the correct graph which represents the optimal solution. B (i) (ii) 26 B 26 24 22 20 24 22 20 18 18 16 16- 14 14 12 10- 8 Optimal Solution A = 7.2, B = 4.4 SA + 2B = 30.4 12 10- 8 6 Optimal Solution A= 6. B=8 3.A + 2B = 34 6 4 4 2 2 A 6 8 10 12 14 16 18 20 4 6 8 10 12 14 16 18 20 (iii) B 26 (iv) B 26 24 24 2 22 22 20 20 18 18 16+ Optimal Solution 14 A=0, B = 14 3A - B = 28 12 10 16- 14 12 1 10+ 8 8 Optimal Solution A = 14, B = 0 SA + 2B = 42 6 6 4 2- 2 A A 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20