Consider the following linear program. Max 3A + 2B s.t. 1A + 1B ≤ 10 3A + 1B ≤ 26 1A + 2B ≤ 16 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 (_) remains or 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 (_) remains or 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 (d)Use this objective coefficient range information to answer parts b and c. The objective coefficient for variable A is _ to _. Since the change in part b is within or outside this range, we know the optimal solution will or will not change. The objective coefficient range for variable B is _ to ___. Since the change in part (c) is within or outside this range, we know the optimal solution will or will not change.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following linear program.

Max	3A	+	2B
s.t.
	1A	+	1B	≤	10
	3A	+	1B	≤	26
	1A	+	2B	≤	16
	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 (_____) remains or 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 (_____) remains or 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

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

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

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