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Homework, Page 623Match the inequality with its graph. State whether or not the boundary is included.

1.

c.

Boundary is included.

3x

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Homework, Page 623Match the inequality with its graph. State whether or not the boundary is included.

5.

e.

Boundary is included.

22y x

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 3

Homework, Page 623Graph the inequality. State the boundary of the region.

9.

Boundary:

2 5 7x y

2 5 7x y

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Homework, Page 623Graph the inequality. State the boundary of the region.

13.

Boundary:

2 2 9x y 2 2 9x y

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Homework, Page 623Solve the system of inequalities.

17. 5 3 1

3 4 18

x y

x y

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Homework, Page 623Solve the system of inequalities.

21.2

2 2 4

y x

x y

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Homework, Page 623Solve the system of inequalities.

25. 5 2 20

2 3 18

2

0

0

x y

x y

x y

x

y

x

y

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Homework, Page 623Write a system of inequalities whose solution is the region shaded in the given figure. All boundaries are included..

29.3 5 1

4 0 20 3 3

6 4 20.5 5

1.5 9

0

0

m

m

y x

y x

x

y

(4, 3)

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 9

Homework, Page 623Find the minimum and maximum of the objective function, if they exist, subject to the constraints.

33. Objective function: 7 4

Constraints :

5 60

6 60

4 6 204

0, 0

f x y

x y

x y

x y

x y

5 60

4 6 204

5 1 60 1 0 6

4 6 204 0 1 30

x y

x y

6 60

4 6 204

1 6 60 1 0 48

4 6 204 0 1 2

x y

x y

7 4

0,60 0 240 240

6,30 42 120 162, minimum

48,2 336 8 342

60,0 420 0 420

No maximum

f x y

f

f

f

f

x

y

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 10

Homework, Page 62337. Pearson’s Metal mines two ores, R and S. The company extracts minerals A and B from each type of ore. It costs $50 per ton to extract 80 lb of A and 160 lb of B from ore R. It costs $60 per ton to extract 140 lb of A and 50 lb of B from ore S. Pearson’s must produce at least 4000 lb of A and 3200 lb of B. How much of each ore should be processed to minimize cost? What is the minimum cost?

Let be the amount of ore R

Let be the amount of ore S

80 140 4000

160 50 3200

80 140 4000 1 0 13.478

160 50 3200 0 1 20.870

, 50 60 50,0 50 50 0 $2500

x

y

x y

x y

C x y x y C

0,64 0 60 64 $3840

14,21 50 14 60 21 700 1260 $1960

Processing 14 tons of R and 21 tons of S is the minimum cost option at $1,960.

C

C

x

y

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Homework, Page 62341. The graph of a linear inequality is a half-line. Justify your answer.

False, the graph of a linear inequality is a half-plane.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 12

Homework, Page 623Refer to the following linear programming problem.

45. Which of the following is not a corner point?

a. (0, 0)

b. (5, 0)

c. (0,4)

d. (3, 4)

e (3.6, 2.8)

Objective function: 5 10

Constraints: 2 10

3 12

, 0

f x y

x y

x y

x y

2 10 0,10 , 5,0

3 12 0,4 , 12,0

, 0 0,0

2 10

2 6 24

5 14 2.8, 3.6 3.6,2.8

x y

x y

x y

x y

x y

y y x

x

y

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Homework

Homework Assignment #14 Review Sections 2.4 – 2.8, 3.1 – 3.6, 7.1 – 7.5 Page 626, Exercises: 1 – 81(EOO) Midterm Exam next time