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
