copyright © 2012 pearson education, inc. all rights reserved chapter 3 linear programming: the...

Copyright © 2012 Pearson Education, Inc. All rights reserved

Chapter 3

Linear Programming:

The Graphical Method


3.1

Graphing Linear Inequalities

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Figure 1

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Figure 2


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Figure 3


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Figure 4


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Your Turn 1


Graph 3 2 18.x y

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Your Turn 2


Graph the feasible region for the system 3 4 12

0

x y

x y

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Figure 8


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Figure 9


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Figure 10



3.2

Solving Linear Programming Problems

Graphically


Figure 11

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Figure 12


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Figure 13


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Figure 14


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Figure 15


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Figure 16



3.3

Applications of Linear Programming

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Figure 17


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Example 2 This question will be solved in Chapter 4

using the Simplex Method.

A 4-H member raises only goats and pigs. She wants to raise no

more than 16 animals, including no more than 10 goats. She

spends $25 to raise a goat and $75 to raise a pig, and she has

$900 available for this project. Each goat produces $12 in profit

and each pig $40 in profit. How many goats and how many pigs

should she raise to maximize total profit?


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Example 2 continued


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Figure 18 - Graph of the feasible region


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Figure 19


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Figure 20


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Figure 21


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Figure 22


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Chapter 3 Review

Extended Application: Sensitivity Analysis

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Figure 23


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Figure 24


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Figure 25


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Figure 26


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Figure 27


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