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Homework, Page 623. Match the inequality with its graph. State whether or not the boundary is included. 1. c. Boundary is included.. Homework, Page 623. Match the inequality with its graph. State whether or not the boundary is included. 5. e. Boundary is included.. - PowerPoint PPT Presentation
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 1
Homework, Page 623Match the inequality with its graph. State whether or not the boundary is included.
1.
c.
Boundary is included.
3x
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 2
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
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 4
Homework, Page 623Graph the inequality. State the boundary of the region.
13.
Boundary:
2 2 9x y 2 2 9x y
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 5
Homework, Page 623Solve the system of inequalities.
17. 5 3 1
3 4 18
x y
x y
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 6
Homework, Page 623Solve the system of inequalities.
21.2
2 2 4
y x
x y
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 7
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
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 8
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
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 11
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
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 7- 13
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