Mathematical Applications for the Management, Life, and Social Sciences

1095 Pages·120.582 MB·English

by  Harshbarger R.J., Reynold J.J.

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
06234_fm_hr_i-1.indd 2 9/27/11 4:15 PM
Buy the way you want and save
Get the best grade in the shortest time possible!
Now that you’ve bought the textbook . . .
Get a break on the study materials designed for your
course! Visit CengageBrain.com and search for your text-
book to find discounted print, digital and audio study tools
that allow you to:
• Study in less time to get the grade you
want using online resources such as chapter
quizzing, flashcards, and interactive study tools.
• Prepare for tests anywhere, anytime
• Practice, review, and master course
concepts using printed guides and manuals that
work hand-in-hand with each chapter of your
textbook.
Your First Study Break
www.CengageBrain.com
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_end_ptg01_hr_2-4.indd 2 9/30/11 8:52 AM
Index of Selected Applications
Business and Management Marketing, 440
Accounting, 209, 520 Market share, 341, 696
Advertising, 9, 28, 46, 77, 94, 172–173, 267, 296, 337, 361, 365, 458, 484, Material supply, 201–202
520, 555, 565, 597, 604, 611, 616, 644–645, 649, 662, 681, 725, 763, Minimizing average cost, 666–667, 671–672, 695, 696
773, 817, 826, 915, 918 Minimizing costs, 273–274, 301–302, 676–677, 681–682, 687, 691, 694
Agribusiness, 237–239, 263–264, 280, 368, 889 Oil industry, 208, 448, 457, 729–730, 754, 793, 807–808, 818, 828
Average cost, 46, 50, 649, 666–667, 671–672, 691, 695, 696, 865 Operating leverage, 183
Break-even point, 59, 63, 146–147 Organizational growth, 355–356, 361
Budgeting, 295 Package design, 35, 39
Business risk, 183 Parking costs, 555
Capital investment, 589, 695, 721, 731, 872, 875, 877, 890, 894, 916 Parts delivery, 448
Capital value, 849, 853, 866 Parts manufacturing, 244–245
Cellular phones, 34–35, 94, 174, 366, 475, 490, 491, 590, 611–612, 613, Population and labor force, 187–188
617, 682 Postal restrictions and rates, 77, 163, 164–165, 567, 677–678
Committees, 471, 472, 487 Pricing, 83, 105, 207, 278, 323–324, 338, 509, 604, 649, 681, 699, 789, 919
Company growth, 28, 675–676 Printing, 696, 919
Competition, 235, 491, 736, 919 Product design, 696
Construction, 279, 295, 297 Product reliability, 336, 359, 436, 497, 508, 533, 815, 818, 850–851, 853
Cost, 76, 77, 106–108, 119, 121, 145, 159–161, 164, 165, 247, 278, 306, Production, 197–198, 208–209, 251, 273–274, 305, 314, 318–319, 611,
319–320, 360, 568, 579, 590, 630, 631, 634–635, 754, 777–778, 649, 662, 721, 725, 731, 763, 799–800, 818, 861, 875, 877–878,
780–781, 793, 823, 826, 840, 860, 866, 873, 913, 915 889–890, 904, 910, 912–913, 915
Cost-benefit, 50, 178, 549–550, 555, 566, 590, 597, 691 Production costs, 165, 649, 681, 687, 698
Customer service, 818, 853 Productivity, 487, 555, 565, 630, 649, 661, 680, 691, 695, 696, 763, 793, 795
Diminishing returns, 661, 662, 695 Profit, 34, 50, 58–59, 63, 64, 76, 77, 106–107, 119–120, 121, 134, 135,
Egg production, 207 144, 256, 360, 378, 391, 554, 580, 630, 631, 691, 730–731, 780–781,
Employee age and gender, 438–439, 447, 448 793, 826, 878
Employee benefits and compensation, 87, 256, 378, 475, 497, 905 Profit maximization, 148–149, 177, 268–269, 279, 307, 319, 668–670,
Employee credentials, 533 672–674, 680, 695, 776–778, 899, 903, 904, 915
Employee evaluation, 49, 476 Property and real estate, 445, 508, 679–680, 766–767
Expense accounts, 197 Purchasing, 64
Franchise growth, 764 Purchasing electrical power, 869
Fraud, 439, 536 Quality control, 436, 440, 457, 458, 460, 470, 473, 475, 476, 487, 495, 497,
Freight logistics, 229–231 498, 520, 529, 536, 853, 865, 866
Fundraising, 124 Rentals, 34, 64, 105, 145, 221, 297, 519–520
Hospital administration, 123 Return to sales, 633, 881
Hotel pricing, 699 Revenue, 34, 40, 50, 77, 106–107, 121, 145, 207, 297, 355, 360, 533, 536,
Human resources, 533 554, 555, 579, 586–587, 589, 597, 604, 608–609, 610, 616, 630, 631,
Industrial accidents, 441 649, 712, 734–735, 777–778, 792, 793, 828, 839, 866, 913
Industrial consolidation, 337 Revenue maximization, 141–143, 177, 271, 619, 665–666, 671, 681, 682,
Industrial waste, 529 691, 694, 695, 737–738, 742
Insurance, 15, 49, 476, 497, 509, 513–514, 520, 529, 532, 533 Rewards for employees, 475
Interdepartmental costs, 247 Safety, 440, 731, 741–742
Inventory, 197–198, 439, 529, 678–679, 682, 696, 826, 902 Salaries, 15, 64, 378, 422, 447, 509
Job bids, 448 Sales, 28, 46, 196, 337, 365, 438, 471, 475, 509, 520, 533, 554–555, 565,
Job effectiveness, 49 597, 604, 611, 616, 649, 662, 680, 681, 715, 725, 773, 789, 817,
Joint cost, 888 826, 915
Labor efficiency and scheduling, 198, 307, 580 Sales decay, 353, 359, 365
Land use, 263–264, 278, 316, 862 Sales growth, 360, 361
Maintenance costs, 458, 865 Scheduling, 277, 295, 296, 304–305, 311–312, 315, 487
Management, 197, 198, 438–439, 440, 448, 471, 475, 533, 536, 698 Shadow prices, 278, 323–324
Manufacturing, 77, 106, 199, 201–202, 213–214, 236, 237–238, 244–245, Shipping, 278, 296, 306–307, 322
251, 262–263, 266–267, 276, 277, 278, 279, 287–291, 295, 296–297, Starbucks stores, 367, 616–617
304–305, 314–315, 316, 318, 319, 453, 520, 904, 913 Surplus, 865
Marginal cost, 619–621, 705–706, 708, 715, 741, 774–776, 879 Telecommunications, 490–491, 836, 839
Marginal demand, 915 Ticket sales, 221
Marginal profit, 621–623 Total income, 817, 826–827
Marginal return to sales, 633, 881 Training, 554
Marginal revenue, 107, 572, 579–580, 594–595, 618, 624, 649, 709, 715, Transportation, 28, 222, 236, 252, 322, 440
751, 754, 760, 763, 772 Unemployment rates, 507
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_end_ptg01_hr_2-4.indd 3 9/30/11 8:52 AM
Unions, 146, 197, 556, 650–651 Finance
Utilities, 164, 209, 239, 245–246, 248, 487, 876, 886 Amortization, 413, 415–416, 419–420, 423, 424, 876
Warranties, 853 Annuities, 46, 394, 395, 403, 406–407, 408, 410, 423, 427–428,
Wilson’s lot size formula, 876 565–566
Wireless service spending, 64 Annuities due, 397, 406, 410–412
Workers and output, 589, 610 APY, 384–385
ATM transaction, 475
Economics
Banks, 84, 279, 471, 475
Balance of trade, 190–191 Bond pricing, 405–406, 412
Cobb-Douglas production function, 872 Bonds, 510
Competitive market, 622, 872 Budgeting, 520
Competitive products, 893 Capital value, 849, 853
Complementary products, 893 College fund, 422, 423, 508, 509
Consumer (personal) spending, 39, 87, 94, 104, 337, 580, 715, 877 Compound interest, 20, 336, 338, 360, 365, 383–384, 385, 386, 389–390,
Consumer price index, 334, 338, 360, 663, 716–717, 755, 773 741, 772, 788–789
Consumer’s surplus, 830–831, 833–834, 835–836, 840, 865 Consumer credit and credit cards, 63, 364, 427, 477
Continuous income streams, 828, 829–830, 834–835, 840, 844, 846, 865 Debt refinancing and payment, 75, 196–197. See also Loans
Demand, 39, 120, 149, 152–153, 165, 177, 354–355, 359, 526, 565, 579, Deferred annuities, 407–408, 412–413
589, 602, 604, 610, 630, 709, 723, 725, 731, 732–734, 738–739, 742, Delinquent accounts, 452–453
796, 826, 860–861, 915 Depreciation, 63, 79, 86, 87, 391, 817
Dependency ratio, 617 Doubling time, 349–350, 385–386
Dow Jones averages, 8–9, 66, 67, 75, 556, 674–675 Earnings, 94, 196, 605, 649, 905
Earnings and race, 87 Future value of annuities, 392–401
Economic dependency ratio, 617, 650 Future value of income stream, 829–830
Economic order quantity, 698 Future value of investments, 329–330, 372, 379–381, 383–384, 423, 712,
Economy models, 252 714–715
Elasticity of demand, 732–734, 738–739 Income stream, 815, 829–830
Gasoline mileage and prices Investing, 20, 28, 35, 59, 64, 98–99, 105, 120, 218–219, 221–222, 223,
Gini coefficient of income, 819, 827 236, 251, 297–298, 327, 329–330, 340–341, 372–373, 384, 393–394,
Gompertz curves, 355–356, 360–361, 790 395, 423, 427–428, 589, 604, 695, 708–709, 731, 789, 793, 876
Gross domestic product, 164, 173, 591, 605, 790 Loans, 50, 105, 221, 413–422, 423
Gross national product, 663 Mortgages and home loans, 19, 69–70, 74–75, 414–415, 427, 428, 876–877
Income distribution, 63, 822, 827, 846, 861, 865 Mutual funds, 475
Indifference curves, 874–875 Perpetuities, 565–566, 849, 853
Inflation, 332, 391, 741, 744, 766–767, 790–791 Present value, 372, 381
International trade, 196 Present value of annuities, 401–404, 408
Job factors, 9, 49 Property and real estate, 445, 508, 679–680, 766–767
Leontief input-output models, 237–249 Purchasing power, 716
Lorenz curves, 819, 827 Retirement planning, 87, 475, 868, 905, 915
Marginal demand, 891 Savings, 779, 781, 865, 914–915
Marginal productivity, 889, 910 Simple interest, 39, 50, 371–373, 376–377
Marginal return to sales, 663 Sinking funds, 396, 423
Marginal utility, 887 Stock market, 6–7, 20–21, 338, 360, 487, 522
Market equilibrium, 109–110, 116, 120, 121, 149–150, 152–153, 177, Taxes, 15, 16, 63, 64, 66, 67, 69, 94, 165–166, 168–169, 174, 255–256,
361, 793 555, 559–560, 566, 736–738, 739–740, 742, 915–916
Monopoly market, 669, 831–832 Trusts, 411, 412, 425, 847, 849
National consumption, 610, 778–779, 781, 793 Venture capital, 204–205, 231–232
National debt, 337, 359, 715
Oil imports, 807–808, 818, 828 Life Science
Open and closed economies, 239–245, 248 Adrenalin response, 566, 598
Optimization in business, 280, 634 Age-sleep relationship, 87
Personal income, 337–338, 488, 585–586, 605, 716, 754, 774, 809, 819, AIDS cases, 177, 391, 447
840, 860, 866 Allometric relationships, 164, 590, 601, 731, 788, 793
Present value, 828, 829, 846, 860 Atmospheric pressure, 790
Producer’s surplus, 832–834, 836, 840, 846, 865 Bacterial growth, 105, 237, 327, 336, 391, 789, 793
Purchasing power, 332, 334, 359, 360, 364 Bee ancestry and reproduction, 237, 377
Social security fund, 75, 127, 131–132, 135, 580, 598, 674, 675, 764, 826 Biology, 533
Supply, 120, 177, 192–193, 359–360, 631, 709, 731, 796, 860–861 Birth control, 458, 520, 540
Travel and tourism, 135, 164, 682, 716, 846, 916 Birth defects, 494, 496
Unemployment, 778 Birth weights, 509
Utility, 874, 877, 909, 912, 914, 915 Blood flow, 726, 727–728, 731
Work force, 447 Blood pressure, 529, 540, 715–716, 773
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_end_ptg01_hr_2-4.indd 4 9/30/11 8:52 AM
10
n
o
i
t
i
d
e
Mathematical
Applications
for the Management, Life,
and Social Sciences
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 1 9/27/11 4:15 PM
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 2 9/27/11 4:15 PM
10
n
o
i
t
i
d
e
Mathematical
Applications
for the Management, Life,
and Social Sciences
Ronald J. Harshbarger
University of South Carolina, Beaufort
James J. Reynolds
Clarion University of Pennsylvania
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 3 9/27/11 4:15 PM
Mathematical Applications for the © 2013, 2009, Brooks/Cole, Cengage Learning
Management, Life, and Social Sciences,
ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
Tenth Edition
may be reproduced, transmitted, stored, or used in any form or by any means
Ronald J. Harshbarger
graphic, electronic, or mechanical, including but not limited to photocopying,
James J. Reynolds
recording, scanning, digitizing, taping, Web distribution, information networks,
Publisher: Richard Stratton or information storage and retrieval systems, except as permitted under
Section 107 or 108 of the 1976 United States Copyright Act, without the prior
Senior Development Editor: Laura Wheel
written permission of the publisher.
Senior Editorial Assistant: Haeree Chang
Media Editor: Andrew Coppola For product information and technology assistance, contact us at
Senior Marketing Manager: Barb Bartoszek Cengage Learning Customer & Sales Support, 1-800-354-9706.
Marketing Coordinator: Michael Ledesma For permission to use material from this text or product,
submit all requests online at www.cengage.com/permissions.
Marketing Communications Manager:
Further permissions questions can be emailed to
Mary Anne Payumo [email protected].
Content Project Manager: Cathy Brooks
Art Director: Jill Ort Haskell Library of Congress Control Number: 2011932871
Manufacturing Planner: Doug Bertke
Student Edition:
Rights Acquisitions Specialist: ISBN-13: 978-1-133-10623-4
Shalice Shah-Caldwell ISBN-10: 1-133-10623-4
Production Service: Lachina Publishing Services Instructor’s Edition:
Text Designer: Rokusek Design, Inc. ISBN-13: 978-1-133-10847-4
ISBN-10: 1-133-10847-4
Cover Designer: Rokusek Design, Inc.
Cover Image: www.shutterstock.com
Brooks/Cole
Compositor: Lachina Publishing Services
20 Channel Center Street
Boston, MA 02210
USA
Cengage Learning is a leading provider of customized learning solutions
with office locations around the globe, including Singapore, the United
Kingdom, Australia, Mexico, Brazil and Japan. Locate your local office at
international.cengage.com/region.
Cengage Learning products are represented in Canada by Nelson Education,
Ltd.
For your course and learning solutions, visit www.cengage.com.
Purchase any of our products at your local college store or at our preferred
online store www.cengagebrain.com.
Instructors: Please visit login.cengage.com and log in to access instructor-
specific resources.
Printed in the United States of America
1 2 3 4 5 6 7 15 14 13 12 11
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 4 9/27/11 4:15 PM
Contents
Preface ix
0 Algebraic Concepts  2 2 Quadratic and Other Special Functions  125
0.1 Sets  3 Warm-up 126
0.2 The Real Numbers  10 2.1 Quadratic Equations  127
0.3 Integral Exponents  16 2.2 Quadratic Functions: Parabolas  136
0.4 Radicals and Rational Exponents  21 2.3 Business Applications Using
Quadratics  146
0.5 Operations with Algebraic Expressions  28
2.4 Special Functions and Their Graphs  153
0.6 Factoring  35
2.5 Modeling; Fitting Curves to Data with
0.7 Algebraic Fractions  40
Graphing Utilities (optional)  165
Key Terms and Formulas  46
Key Terms and Formulas  175
Review Exercises  48
Review Exercises  176
Chapter Test 50
Chapter Test  179
Extended Applications & Group Projects  52
Extended Applications & Group Projects  181
Campaign Management
An Inconvenient Truth • Body-Mass
Index (Modeling) • Operating Leverage and
Business Risk
1 Linear Equations and Functions  53
Warm-up  54
1.1 Solutions of Linear Equations and 3 Matrices  184
Inequalities in One Variable  55
Warm-up 185
1.2 Functions  65
3.1 Matrices  186
1.3 Linear Functions  78
3.2 Multiplication of Matrices  199
1.4 Graphs and Graphing Utilities  88
3.3 Gauss-Jordan Elimination: Solving Systems
1.5 Solutions of Systems of Linear
of Equations  209
Equations  95
3.4 Inverse of a Square Matrix; Matrix
1.6 Applications of Functions in Business and
Equations  224
Economics  106
3.5 Applications of Matrices: Leontief Input-
Key Terms and Formulas  116
Output Models  237
Review Exercises  118
Key Terms and Formulas  249
Chapter Test  121
Review Exercises  250
Extended Applications & Group Projects  123
Chapter Test  252
Hospital Administration • Fundraising
Extended Applications & Group Projects  255
Taxation • Company Profits after Bonuses
and Taxes
v
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 5 9/27/11 4:15 PM
vi contents
6.5 Loans and Amortization  413
4 Inequalities and Linear Programming  257
Key Terms and Formulas  421
Warm-up 258
Review Exercises  422
4.1 Linear Inequalities in Two Variables  259
Chapter Test  425
4.2 Linear Programming: Graphical
Extended Applications & Group Projects  427
Methods  268
Mail Solicitation Home Equity Loan: Is
4.3 The Simplex Method: Maximization  279
This a Good Deal? • Profit Reinvestment •
4.4 The Simplex Method: Duality and Purchasing a Home
Minimization  298
4.5 The Simplex Method with Mixed
Constraints  307
7 Introduction to Probability  429
Key Terms and Formulas  316
Review Exercises  317 Warm-up 430
Chapter Test  320 7.1 Probability; Odds  431
Extended Applications & Group Projects  322 7.2 Unions and Intersections of Events: One-
Transportation • Slack Variables and Shadow Trial Experiments  441
Prices 7.3 Conditional Probability: The Product
Rule  449
7.4 Probability Trees and Bayes’ Formula  459
7.5 Counting: Permutations and
5 Exponential and Logarithmic Functions  325
Combinations  466
Warm-up 326 7.6 Permutations, Combinations, and
5.1 Exponential Functions  327 Probability  472
5.2 Logarithmic Functions and Their 7.7 Markov Chains  476
Properties  339 Key Terms and Formulas  485
5.3 Solutions of Exponential Equations: Review Exercises  486
Applications of Exponential and
Chapter Test  488
Logarithmic Functions  351
Extended Applications & Group Projects  490
Key Terms and Formulas  362
Phone Numbers • Competition in the
Review Exercises  363
Telecommunications Industry
Chapter Test  365
Extended Applications & Group Projects  367
Starbucks Stores (Modeling) • Agricultural
8 Further Topics in Probability; Data
Business Management
Description  492
Warm-up 493
6 Mathematics of Finance  369 8.1 Binomial Probability Experiments  494
8.2 Data Description  498
Warm-up 370
8.3 Discrete Probability Distributions; The
6.1 Simple Interest; Sequences  371
Binomial Distribution  511
6.2 Compound Interest; Geometric
8.4 Normal Probability Distribution  521
Sequences  378
8.5 The Normal Curve Approximation to the
6.3 Future Values of Annuities  392
Binomial Distribution  529
6.4 Present Values of Annuities  401
Key Terms and Formulas  534
Review Exercises  535
Chapter Test  536
Extended Applications & Group Projects  539
Lotteries • Statistics in Medical Research;
Hypothesis Testing
Copyright 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
06234_fm_hr_i-1.indd 6 9/27/11 4:15 PM