Answered: Consider the following linear program.…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 9E

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Question

Consider the following linear program.

Min	8X	+	12Y
s.t.
	1X	+	3Y	≥	6
	2X	+	2Y	≥	8
	6X	+	2Y	≥	12
	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) = () ______ 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) = () ______ 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 ______ this range, we know the optimal solution ______ change. The objective coefficient range for variable Y is ______ to ______ . Since the change in part (c) is ______ this range, we know the optimal solution ______ change.

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