About the Cover Upon entering the University of Kansas as an undergraduate, Chris Shannon knew she enjoyed mathematics, but she was also interested in a variety of social and political issues One of her mathematics professors recognized this and suggested that she might be interested in taking some economics courses while she was studying mathematics She learned that economics enabled her to combine the rigor and abstraction of mathematics with the exploration of complex and important social issues involving human behavior She decided to add a major in economics to her math major After graduating with B.S degrees in economics and in mathematics, Shannon went on to graduate school at Stanford University, where she received an M.S in mathematics and a Ph.D in economics Her current position as professor in both the mathematics and economics departments at the University of California, Berkeley, represents an ideal blend of the two fields, and allows her to pursue work ranging from developing new tools for analyzing optimization problems to designing new models for understanding complex financial markets The photos on the front cover of this text represent one of her current projects, which explores new models of decision-making under uncertainty and the effects of uncertainty on different markets.* CHRIS SHANNON Economics and Finance University of California, Berkeley Look for other featured applied researchers in forthcoming titles in the Tan applied mathematics series: PETER BLAIR HENRY International Economist Stanford University MARK VAN DER LAAN Biostatistician University of California, Berkeley JONATHAN D FARLEY Applied Mathematician California Institute of Technology NAVIN KHANEJA Applied Scientist Harvard University *Shannon, Chris, and Rigotti, Luca, “Uncertainty and Risk in Financial Markets,” Econometrica, January 2005, 73(1), pp 203–243 Now that you’ve bought the textbook GET THE BEST GRADE IN THE SHORTEST TIME POSSIBLE! Visit www.iChapters.com to view over 10,000 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 pre- and post-tests and personalized study plans • Prepare for tests anywhere, anytime using chapter review audio files that are downloadable to your MP3 player • Practice, review, and master course concepts using printed guides and manuals that work hand-in-hand with each chapter of your textbook Join the thousands of students who have benefited from www.iChapters.com Just search by author, title, or ISBN, then filter the results by “Study Tools” and select the format best suited for you www.iChapters.com Your First Study Break Formulas Equation of a Straight Line Equation of the Least-Squares Line a point-slope form: y Ϫ y1 ϭ m(x Ϫ x1) b slope-intercept form: y ϭ mx ϩ b c general form: Ax ϩ By ϩ C ϭ y ϭ mx ϩ b where m and b satisfy the normal equations nb ϩ (x1 ϩ x2 ϩ ϩ xn)m ϭ y1 ϩ y2 ϩ ϩ yn (x1 ϩ x2 ϩ ϩ xn)b ϩ (x 21 ϩ x 22 ϩ ϩ x 2n )m ϭ x1y1 ϩ x2 y2 ϩ ϩ xnyn Compound Interest A ϭ P(1 ϩ i)n (i ϭ r/m, n ϭ mt) where A is the accumulated amount at the end of n conversion periods, P is the principal, r is the interest rate per year, m is the number of conversion periods per year, and t is the number of years Effective Rate of Interest reff ϭ a1 ϩ r m b Ϫ1 m where reff is the effective rate of interest, r is the nominal interest rate per year, and m is the number of conversion periods per year Future Value of an Annuity Present Value of an Annuity Amortization Formula SϭRc PϭRc Rϭ 11 ϩ i n Ϫ i d Ϫ 11 ϩ i Ϫn i Pi Ϫ 11 ϩ i Ϫn d iS 11 ϩ i2 n Ϫ Sinking Fund Payment Rϭ The Number of Permutations of n Distinct Objects Taken r at a Time P(n, r) ϭ The Number of Permutations of n Objects, Not All Distinct n! , where n1 ϩ n2 ϩ ϩ nm ϭ n n1!n2! nm! C(n, r) ϭ The Number of Combinations of n Distinct Objects Taken r at a Time Expected Value of a Random Variable Bernoulli Trials n! r!1n Ϫ r2! P(A ʝ B) ϭ P(A) и P(B ͉ A) The Product Rule for Probability Bayes’ Formula n! 1n Ϫ r2! P(Ai ͉ E) ϭ P1Ai # P1E Έ Ai P1A1 # P1E Έ A1 ϩ P1A2 # P1E Έ A2 ϩ ϩ P1An # P1E Έ An E(X) ϭ x1 p1 ϩ x2 p2 ϩ ϩ xn pn P(X ϭ x) ϭ C(n, x)pxq nϪx E(X) ϭ np Var(X) ϭ npq X ϭ 1npq (x ϭ 0, 1, 2, , n) EDITION FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES This page intentionally left blank EDITION FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES S T TAN STONEHILL COLLEGE Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Finite Mathematics for the Managerial, Life, and Social Sciences, Ninth Edition S T Tan Senior Acquisitions Editor: Carolyn Crockett Development Editor: Danielle Derbenti Assistant Editor: Catie Ronquillo Editorial Assistant: Rebecca Dashiell © 2009, 2006 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher Technology Project Manager: Ed Costin Marketing Manager: Mandy Jellerichs Marketing Assistant: Ashley Pickering Marketing Communications Manager: Talia Wise Project Manager, Editorial Production: Cheryll Linthicum Creative Director: Rob Hugel For product information and technology assistance, contact us at Cengage Learning & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at cengage.com/permissions Further permissions questions can be e-mailed to permissionrequest@cengage.com Library of Congress Control Number: 2007940270 Art Director: John Walker Print Buyer: Judy Inouye Permissions Editor: Bob Kauser ISBN-13: 978-0-495-38753-4 ISBN-10: 0-495-38753-3 Production Service: Martha Emry Text Designer: Diane Beasley Photo Researcher: Terri Wright Copy Editor: Betty Duncan Brooks/Cole 10 Davis Drive Belmont, CA 94002-3098 USA Illustrator: Jade Myers, Matrix Productions Compositor: Graphic World Cover Designer: Irene Morris Cover Images: Chris Shannon © Cengage Learning; Numbers, George Doyle/Stockbyte/Getty Images; Produce, Dimitri Vervitsiotis/Digital Vision/Getty Images; Chess Strategy © David Arky/Corbis; Stock Traders, Scott Olson/Getty Images News/Getty Images 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 academic.cengage.com Purchase any of our products at your local college store or at our preferred online store www.ichapters.com Printed in Canada 12 11 10 09 08 TO PAT, BILL, AND MICHAEL ANSWERS TO CHAPTER ODD -NUMBERED EXERCISES 13 TX0 ϭ c .6915 d; Current state 0.5 Next state State State 2 State State State .2266 603 State −0.75 .4649 576 15 X2 ϭ c d 424 17 X2 ϭ 19 a – 0.75 0.5 16 27 £ 64 § 17 64 Current state .4082 2.42 14 .8413 11 Ϫ2.03 12 1.42 15 .2417 16 .7333 17 41.3 mph 19 .2646; 9163 b .901 29 .9738 b 21 At least 75 23 ϭ 27.87; ϭ 6.41 25 ϭ 120; Ϸ 10.1 27 a .246 26 0.6% 28 a .050 b .995 Ϫ3 05 a .8 Ϫ2 25 L L Tϭ c R R d c X0 ϭ 21 a Vote is evenly split L c d R d .85 b Democrat 2 29 False Using Technology Exercises 9.1, page 494 b .92 a .2401; 4116; 2646; 0756; 0081 a .9772 b .9772 c .9544 a .0222 b .6085 c .0222 CHAPTER b 1.2; 917 204489 131869 X5 ϭ E.261028U 186814 215800 Manufacturer A will have 23.95% of the market share, manufacturer B will have 49.71% of the market share, and manufacturer C will have 26.34% of the market share Exercises 9.2, page 500 Exercises 9.1, page 490 Regular Yes No Yes Not regular c c 48 d 52 Regular No 11 a Given that the outcome state has occurred, the conditional probability that the outcome state will occur is b .7 State 27 Business: 36.0%, Humanities: 23.8%, Education: 15.0%, Natural Sciences and others: 25.1% 0.44; 4.0064; 2.0016 Yes 25 University: 37%, Campus: 35%, Book Mart: 28%; University: 34.5%, Campus: 31.35%, Book Mart: 34.15% Chapter Before Moving On, page 481 x P(X ؍x) State 23 After one year: 78.8% in the city and 21.2% in the suburbs After two years: 77.7% in the city and 22.3% in the suburbs 30 .9997 .9 13 .6915 20 15.87% 22 €21.54 billion; €0.5389 billion 24 .677 State State 0.66 10 Ϫ1.05 18 $12,000 State −0.42 Next state State Not regular c 118 d 11 13 13 £ 138 § 13 15 19 £ 198 § 19 11 c 75 d 17 81.8% 604 ANSWERS TO CHAPTER ODD -NUMBERED EXERCISES 19 40.8% one wage earner and 59.2% two wage earners; 30% one wage earner and 70% two wage earners 21 72.5% in single-family homes and 27.5% in condominiums; 70% in single-family homes and 30% in condominiums 23 a 31.7% ABC, 37.35% CBS, 30.95% NBC b 333 % ABC, 3313 % CBS, 3313 % NBC 25 25% red, 50% pink, 25% white 27 False Using Technology Exercises 9.2, page 504 b c d ; eventually, only unleaded fuel will be used 27 .25; 50; 75 29 a D G D G ≥ 0 0 b ≥ 0 2045 1319 X5 ϭ E.2610U 1868 2158 25 0 75 0 ¥ 0 325 675 0 ¥ 0 c .675 31 False Exercises 9.3, page 510 Yes c Yes Exercises 9.4, page 519 Yes Yes R: row 1; C: column d , R ϭ 4, and S ϭ 3.4 R: row or row 3; C: column 11 £ 0 4 5 § , R ϭ c d , and S ϭ 4, or £0 5 § , R ϭ c d , and S ϭ 4 13 ≥ 0 0 3 Rϭ c ≥ 0 15 c 19 ≥ 0 23 E0 0 25 a UL L ¥, 2 d and S ϭ c 0 4 0 17 £ 0 0 0 0 0 d , or ¥ 0 11 22 22 U 0 0 11 Strictly determined; a b R: row 1; C: column c d Favors row player 19 a £ Ϫ3 0 Ϫ3 Ϫ5 17 Not strictly determined Ϫ5 § b Robin: row 1; Cathy: column or column c Not strictly determined d Not strictly determined d , and so forth 21 a 0§ 21 ≥ 0 22 22 11 Strictly determined; a b R: row 1; C: column c d Favors row player 15 Not strictly determined ¥, d, S ϭ c d R: row or row 3; C: column 13 Strictly determined; a b R: row 1; C: column c d Favors row player Rϭ c R: row 1; C: column Economy Good Recess Mgmt 0 UL L c d , R ϭ 84 , and S ϭ 2 2 0 0 ¥ Expand Not exp ΄ 50,000 200,000 120,000 150,000 ΅ b Yes 23 a Charley Raises Holds Lowers Raises Roland Holds Lowers ΄ Ϫ1 Ϫ3 Ϫ2 25 True Exercises 9.5, page 530 10 12 0.16 ΅ ANSWERS TO APPENDIX A ODD -NUMBERED EXERCISES b Ϫ2 a 15 a c d Ϫ.3; (a) is most advantageous b Ϫ.35 a c The first pair of strategies c 21 d , 11 P ϭ 14 4, Qϭ 13 P ϭ 47 4, Q ϭ c 72 d , and E ϭ Ϫ17 ; favors column player 15 P ϭ 12 24, Q ϭ c 43 d , and E ϭ Ϫ5; favors column player and E ϭ 2.5; favors row player b A 50 U £ 15 § N 35 N 10 05 § 85 A ϭ Agriculture U ϭ Urban N ϭ Nonagricultural c A 424 U £ 262 § N 314 16 12.5% large cars, 30.36% intermediate-sized cars, 57.14% small cars 17 Strictly determined; R: row 3; C: column 1; value is 4 34 U 95 05 17 a P ϭ 13 A A 85 U £ 10 N 05 18 Strictly determined; R: row 1; C: column 2; value is 19 Strictly determined; R: row 1; C: column 1; value is and Q ϭ c 32 d 20 Not strictly determined 21 Ϫ 41 b E ϭ 0; no 10 22 23 24 1.04 19 a $5714 in hotel stocks; $34,286 in brewery stock b $4857 25 P ϭ 12 4, Q ϭ c 61 d , and E ϭ 12 ; favors row player 21 a 26 P ϭ 12 4, Q ϭ c 229 d , and E ϭ Ϫ 12 , favors column player R C N F ΄ N F 48 65 50 45 ΅ C ϭ Carlton; R ϭ Russell N ϭ local newspaper; F ϭ flier b Russell’s strategy: P Ϸ [.23 77] 91 d Carlton’s strategy: Q Ϸ c 09 Chapter Concept Review Questions, page 533 Probabilities; preceding State; state Regular; columns; equal; positive; TX ϭ X; elements; Absorbing; leave; steps Optimal 10 Saddle point; maximin; row; saddle; minimax; column; saddle Chapter Review Exercises, page 534 Not regular Not regular 3675 £ 36 § 2725 1915 £ 4215 § 387 29 a c d c No No Qϭ c 53 d , and E ϭ 10.8; favors row player b $7 £ 0 11 0 b R: row 1; C; column a units 0§ c Ϫ1; column player b 1.22 units a P ϭ 23 4, Q ϭ c 65 d b 43 ; row player A Exercises A.1, page 541 Yes Yes No Yes Yes 11 No 13 No Yes Q ϭ c 51 d , and E ϭ 1.2; favors row player c 118 d 366 d 634 APPENDIX Regular Regular 54, a Ϫ1 b Maximin; minimax 22 10 , 28 P ϭ 45 13 Chapter Before Moving On, page 535 Distribution; steady-state a Zero-sum 27 P ϭ 101 30 25% compact models; 75% subcompact models n ϫ n; nonnegative; Transition 605 15 Negation 17 Conjunction 10 Yes 19 Conjunction 11 c 74 7 4d 457 13 £ 200 343 12 .457 200 343 c 95 457 200 § 343 5d 21 New orders for manufactured goods did not fall last month .323 14 £ 290 387 323 290 387 323 290 § 387 23 Drinking during pregnancy does not affect both the size and weight of babies 25 The commuter airline industry is not now undergoing a shakeup 606 ANSWERS TO CHAPTER ODD -NUMBERED EXERCISES 27 a Domestic car sales increased over the past year, or foreign car sales decreased over the past year, or both b Domestic car sales increased over the past year, and foreign car sales decreased over the past year c Either domestic car sales increased over the past year or foreign car sales decreased over the past year d Domestic car sales did not increase over the past year e Domestic car sales did not increase over the past year, or foreign car sales decreased over the past year, or both f Domestic car sales did not increase over the past year, or foreign car sales did not decrease over the past year, or both 29 a Either the doctor recommended surgery to treat Sam’s hyperthyroidism or the doctor recommended radioactive iodine to treat Sam’s hyperthyroidism b The doctor recommended surgery to treat Sam’s hyperthyroidism, or the doctor recommended radioactive iodine to treat Sam’s hyperthyroidism, or both 31 a p ٙ q b p Ք q c ϳp ٙ ϳq d ϳ(ϳq) 33 a Both the popularity of prime-time soaps and prime-time situation comedies did not increase this year b The popularity of prime-time soaps did not increase this year, or the popularity of prime-time detective shows decreased this year, or both c The popularity of prime-time detective shows decreased this year, or the popularity of prime-time situation comedies did not increase this year, or both d Either the popularity of prime-time soaps did not increase this year or the popularity of prime-time situation comedies did not increase this year Exercises A.2, page 544 p T T F F ϳq F T F T q T F T F p ٚ ϳq T T F T 11 p T T F F q T F T F pٚq T T T F q T T F F T T F F r T F T F T F T F ϳ( p ٚ q) F F F T ( p ٚ q) ٙ ϳ( p ٚ q) F F F F 13 p T T T T F F F F pٚq T T T T T T F F pٚr T T T T T F T F ( p ٚ q) ٙ (p ٚ r) T T T T T F F F 15 p T T T T F F F F q T T F F T T F F pٙq T T F F F F F F r T F T F T F T F ϳr F T F T F T F T ( p ٙ q) ٚ ϳr T T F T F T F T 17 p T T T T F F F F q T T F F T T F F ϳq F F T T F F T T r T F T F T F T F p ٙ ϳq F F T T F F F F pٙr T F T F F F F F ( p ٙ ϳq) ٚ (p ٙ r) T F T T F F F F 19 16 rows ϳp F T p T F Exercises A.3, page 548 ϳ(ϳp) T F ϳq Ǟ p; q Ǟ ϳp; ϳp Ǟ q p Ǟ q; ϳp Ǟ ϳq; ϳq Ǟ ϳp ϳp F T p T F p T T F F p ٚ ϳp T T Conditional: If it is snowing, then the temperature is below freezing Biconditional: It is snowing if and only if the temperature is below freezing q T F T F ϳp F F T T pٚq T T T F ϳp ٙ ( p ٚ q) F F T F ϳq F T F T pٚq T T T F p ٙ ϳq F T F F ( p ٚ q) ٙ (p ٙ ϳq) F T F F p T T F F q T F T F Conditional: If the company’s union and management reach a settlement, then the workers not strike Biconditional: The company’s union and management will reach a settlement if and only if the workers not strike False 11 False 13 It is false when I not buy the house after the owner lowers the selling price 15 p T T F F q T F T F pǞq T F T T ϳ( p Ǟ q) F T F F ANSWERS TO APPENDIX A ODD -NUMBERED EXERCISES Exercises A.4, page 552 17 p T T F F pǞq T F T T q T F T F ϳ( p Ǟ q) F T F F ϳ( p Ǟ q) ٙ p F T F F 19 p T F pٙp T F p T F p T T F F ϳp F F T T q T F T F ϳq F T F T p Ǟ ϳq F T T T ( p Ǟ ϳq) Ք ϳp F T F F p T T T T F F F F 21 p T T F F 607 q T F T F ϳp F F T T ϳq F T F T pǞq T F T T ϳq Ǟ ϳp ( p Ǟ q) ǟǞ (ϳq Ǟ ϳp) T T F T T T T T ( p ٙ q) ٙ r T F F F F F F F 23 p T T F F pٙq T F F F q T F T F pٚq T T T F q T T F F T T F F ( p ٙ q) Ǟ ( p ٚ q) T T T T r T F T F T F T F qٙr T F F F T F F F pٙq T T F F F F F F p ٙ (q ٙ r) T F F F F F F F 25 p T T T T F F F F q T T F F T T F F pٚq T T T T T T F F r T F T F T F T F ϳr F T F T F T F T ( p ٚ q) Ǟ ϳr F T F T F T T T 27 p T T T T F F F F q T T F F T T F F r T F T F T F T F qٚr T T T F T T T F 29 Logically equivalent 31 Logically equivalent p Ǟ (q ٚ r) T T T F T T T T p T T F F q T F T F pٙq T F F F p T T T T F F F F q T T F F T T F F r T F T F T F T F qٙp T F F F pٚq T T T T T T F F pٚr T T T T T F T F qٙr T F F F T F F F p ٚ (q ٙ r) T T T T T F F F ( p ٚ q) ٙ ( p ٚ r) T T T T T F F F 33 Not logically equivalent Tautology 11 Tautology 13 Tautology 35 Not logically equivalent 37 a p Ǟ ϳq d p Ǟ ϳq b ϳp Ǟ q e p ǟǞ ϳq c ϳq ǟǞ p 15 Tautology 17 Neither 19 ϳ( p ٙ q): The candidate does not oppose changes in the Social Security system, or the candidate does not support immigration reform ϳ( p ٚ q): The candidate does not oppose changes in the Social Security system, and the candidate does not support immigration reform 608 ANSWERS TO APPENDIX C ODD -NUMBERED EXERCISES 21 [ p ٙ (q ٚ ϳq) ٚ ( p ٙ q)] ⇔ p ٙ t ٚ ( p ٙ q)] ⇔ p ٚ ( p ٙ q) 23 ( p ٙ ϳq) ٚ ( p ٙ ϳr) ⇔ p ٙ (ϳq ٚ ϳr) By law 11 By law 14 Valid 11 Valid 17 p Ǟ q; invalid ϳp І ϳq A B ~r r ~p 11 p q r s ~q ~p Valid 13 Valid 15 Invalid A 19 p ٚ q; valid ϳp Ǟ ϳq Іp 21 p Ǟ q; invalid qǞr r B q By law 10 By law Invalid r p By law Exercises A.5, page 557 Valid q 25 ( p ٙ ϳ(q ٙ r) ⇔ p ٙ (ϳq ٚ ϳr) ⇔ ( p ٙ ϳq) ٚ ( p ٙ ϳr) Valid p A B 13 p ٙ [ϳq ٚ (ϳp ٙ q)]; p ٙ ϳq 23 b 15 p ٙ [ϳp ٚ q ٚ (q ٙ r)]; p ٙ q Іp APPENDIX C Exercises, page 571 25 p T T F F q T F T F pǞq T F T T ϳq F T F T ϳp F F T T Exercises A.6, page 560 p ٙ q ٙ (r ٚ s) [( p ٙ q) ٚ r] ٙ (ϳr ٚ p) [( p ٚ q) ٙ r] ٚ (ϳp) ٚ [ϳq ٙ ( p ٚ r ٚ ϳr)] log2 64 ϭ 1.0792 13 ln 1x y z 19 x ϭ 32 25 Ϫ0.0912 log3 91 ϭ Ϫ2 1.2042 11 ln a2b3 15 x ϭ 21 x ϭ 113 log32 ϭ 35 17 x ϭ 10 23 5.1986 27 Ϫ8.0472 29 Ϫ4.9041 INDEX Abscissa, Absorbing state, 505 Absorbing stochastic matrix, 505 Amortization, 287–289 formula, 287 schedule, 288 Annuity, 276 certain, 276 compound amount factor, 277 future value, 278 ordinary, 276 present value, 279 simple, 276 term, 276 Arithmetic progression, 300–302 common difference, 300 nth term, 300 sum, 301 Augmented matrix, 78 Average, 427 Axes, Basic variables, 203 Bayes’ theorem, 402–405 Bernoulli trials, 452–459 Binding constraints, 194 Binomial distribution, 452–459 approximation by a normal distribution, 472–475 binomial trials, 453 mean, 457 standard deviation, 457 variance, 457 Binomial experiment, 453 Binomial random variable, 455 Binomial trials, 453 Birthday problem, 384–385 Book value, 30, 304 Bounded solution set, 160 Break-even analysis, 40–43 Break-even point, 41 Cartesian coordinate system, 2–4 abscissa, axes, ordered pair, ordinate, quadrants, Central limit theorem, 475 Chebychev’s inequality, 444–446 Circle, Column matrix, 102 Column vector, 102 Combinations, 340–342 Complement of a set, 317 Compound interest, 259–262 See also Interest Conditional probability, 388–393 Connectives, 539, 544–547 Continuous compound interest, 262–263 Continuous probability distribution, 462 Continuous random variable, 419, 462 Coordinates, Corner point, 174 Cost function, 30 Counting problem, 323 Current state, 484 Demand curve, 31 Demand equation, 31 Demand function, 31 De Morgan’s laws, 318, 549 Dependent system, 70 Dependent variable, 28 Depreciation book value, 30, 304 double-declining balance, 304–305 linear, 30 simple, 30 sum-of-the-years’-digits, 307 Deviations, 441 Disjoint sets, 317 Disjunction, 539 Distance formula, Distribution vector, 488 Domain, 28 Dual problem, 228 Effective rate of interest, 263 Empty set, 315 Equation of a circle, Equations of straight lines, 17 Equilibrium price, 44 quantity, 44 Equivalent system, 76 Events, 354–356 independent, 395–398 mutually exclusive, 356, 363 probability of, 362–366 simple, 363 union of, 355 Expected value of a binomial random variable, 457 of a game, 524 of a random variable, 428 Experiment, 354 event, 354 outcome, 354 sample point, 354 sample space, 354 Factorial, 337 Fair game, 432, 517, 522 Feasible set, 172 Feasible solution, 172, 203 Finite sample space, 354 Finite stochastic process, 393 Fixed costs, 31 Function, 27 cost, 31 demand, 31 dependent variable, 28 domain, 28 independent variable, 28 linear, 28 objective, 164 probability, 363 probability density, 462 profit, 30 range, 28 revenue, 30 Fundamental theorem of duality, 228 Future value, 265 Gambler’s ruin, 506–508 Game theory, 512–518, 521–529 fair game, 432, 522 games with mixed strategies, 521–528 expected value, 524–526 optimal strategies, 516 maximin strategy, 514 minimax strategy, 514 mixed strategy, 522 nonstrictly determined game, 526 optimal strategy, 516 payoff matrix, 513 pure strategy, 516 saddle point, 516 strictly determined game, 516 two-person games, 512–513 value of a game, 523 zero-sum game, 512 Gauss–Jordan elimination method, 75–85, 91–96 equivalent system, 76 row operations, 80 steps in, 82 Generalized multiplication principle, 332 Genetics, 508–509 Geometric progression, 302–304 common ratio, 302 nth term, 302 sum, 304 Graphing linear inequalities, 156–161 Half-planes, 156 Histogram, 421–422 610 INDEX Identity matrix, 117 Inconsistent system, 70 Independent events, 395–398 Independent variable, 28 Input–output analysis, 141–146 Intercepts, 15 Interest compound, 259–262 formula, 260 future value, 265 present value, 265 principal, 260 continuous compound, 262–263 conversion period, 259 rate effective, 263 nominal, 259 simple, 258–259 accumulated amount, 258 formula, 258 Internal consumption matrix, 143 Intersection of lines, 40–46 Intersection of sets, 317 Inverse of a matrix, 128 Irrational number, 564 Isoprofit line, 173 Least-squares line, 52 Leontief, Wassily, 67, 141 Leontief input–output model, 141–146 input–output matrix, 142 internal consumption matrix, 143 Linear depreciation, 30–31 Linear equations, 12–17 general form, 17 in n variables, 72 intercepts, 15 point-slope form, 13 slope, 10 slope-intercept form, 15 vertical lines, 12, 17 Linear function(s), 28–33 break-even analysis, 40–43 demand and supply curves, 31–33 simple depreciation, 30–31 Linear inequality, 156–161 Linear programming corner point, 174 feasible set, 172 feasible solution, 172, 203 graphical solution, 172–178 linear constraints, 172 method of corners, 174 objective function, 164 optimal solution, 172 problem, 164, 202 basic solution, 204 dual, 228 existence of a solution, 174 nonstandard, 242–250 primal, 228 standard, 202, 226, 242 simplex method, 202–216, 226–234, 242–250 basic variables, 202 nonbasic variables, 203 nonstandard problems, 242 optimal solution(s), 202 pivot column, 205 pivot element, 205 pivot row, 205 simplex tableau, 206 slack variables, 202 standard maximization problem, 202 standard minimization problem, 227 steps in, 207, 246 theorem, 174 Lines See Linear equations Logarithms, 567–571 Logic, 537–561 argument, 533–554 conclusion, 554, 553 conditional statement, 544 converse, 545 contrapositive, 545 inverse, 545 connectives, 539 biconditional, 547 conditional, 544 conjunction, 539 disjunction, 539 exclusive disjunction, 540 inclusive disjunction, 539 negation, 540 contradiction, 550 hypothesis, 544 laws, 549–551 logical equivalence, 546, 551 logical variants, 545 order of precedence, 548 proposition, 553 switching networks, 558 tautology, 550 truth tables, 542–544 Market equilibrium, 43–46 Markov chains, 484–489 absorbing, 505 state, 505 stochastic matrix, 505 current state, 484 regular, 496 steady-state distribution vector, 495 steady-state matrix, 496 stochastic matrix absorbing, 505 regular, 486 transition matrix, 485 transition probabilities, 485 Mathematical model, 26 Matrix, 102 absorbing stochastic, 505 addition, 105 associative law, 105 commutative law, 105 augmented, 78 coefficient, 78 column, 102 cost, 118 dimension, 102 elements, 102 entries, 102 equality, 103 equation, 106 identity, 117 ijth entry (aij), 102 input–output, 142 internal consumption, 143 inverse, 128 inverse of a ϫ matrix, 131 multiplication, 113–119 associative law, 117 distributive law, 117 nonsingular, 128 pivot element, 81 product, 114 regular stochastic, 486 row, 102 row-reduced form, 79 scalar product, 106 singular, 128 size, 102 square, 102 steady-state, 496 subtraction, 104 transition, 486 transpose, 106 zero, 105 Maximin strategy, 514 Mean, 427 Median, 435 Method of corners, 174 Method of least squares, 51–55 least-squares line, 52 normal equations, 53 principle, 52 regression line, 52 scatter diagram, 52 Minimax strategy, 514 Mixed constraints, 242 Mixed strategy, 522 Mode, 435 Modeling, 26–27 Multiplication principle, 329–333 Mutually exclusive events, 356, 363 Natural numbers, 564 Nonbasic variables, 203 Nonstandard linear programming problems, 242–250 INDEX Normal approximation of binomial distribution, 472–475 Normal curve, 463 Normal distribution, 463 Normal equations, 52 Number line, Objective function, 164 Odds, 432–433 Optimal solution, 172 Optimal strategy, 514–519, 526 Ordered pair, Ordinary annuity, 276 Ordinate, Origin, Outcome, 354 Parallel lines, 12 Parameter, 69 Partition, 403 Permutations, 335–340 Perpendicular lines, 14 Pivot column, 205 Pivot element, 205 Pivoting, 81 Pivot row, 205 Point-slope form, 13 Present value, 265 Primal problem, 228 Principle of least squares, 52 Probability addition principle, 365 a posteriori, 402 a priori, 402 Bayes’ theorem, 403 Bernoulli trials, 452–459 binomial distribution, 455 binomial experiment, 453 conditional, 388–393 continuous probability distribution, 462 counting techniques, 329–333, 381–384 density function, 463 distribution, 363, 419–420 elementary event, 363 empirical, 363 of an event, 362–365 expected value, 428 experiment, 354 event, 354 outcome, 354 finite stochastic process, 393 function, 363 independent event, 395 mutually exclusive events, 356, 363 partition, 403 product rule, 391 properties, 371–374 relative frequency, 363 rule of complements, 374 sample point, 354 sample space, 354 event, 354 finite, 354 partition, 403 reduced, 389 uniform, 364 simple event, 363 transition, 485 tree diagram, 303, 339, 356–358, 393–395 Product rule, 391 Profit function, 30 Pure strategy, 522 Quadrant, Random variable, 418 binomial, 455 continuous, 419, 462 expected value, 428 finite discrete, 419 infinite discrete, 419 probability distribution of, 419 standard deviation of, 443 standard normal, 464 variance, 441 Range, 28 Rational numbers, 564 Real number line, Real number system, 564–565 integers, 564 irrational numbers, 564 natural numbers, 564 rational numbers, 564 whole numbers, 564 Regular Markov chain, 496 Regular stochastic matrix, 498 Relative frequency, 363 Revenue function, 30 Roster notation, 314 Roulette, 431 Row matrix, 102 Row operations, 80–81 Row-reduced form, 79 Saddle point, 516 Sample space, 354 finite, 354 reduced, 389 uniform, 364 Scalar, 106 Scalar product, 106 Scatter diagram, 52 Sensitivity analysis, 185–194 binding constraints, 194 changes in the objective function coefficients, 186–189 changes in the right-hand side constants, 189–191 shadow prices, 191 611 Set(s), 314–319 complement, 317 definition, 314 De Morgan’s laws, 318, 549 disjoint, 317 elements, 314 empty, 315 equal, 314 intersection, 317 members, 314 notation roster, 314 set-builder, 314 number of elements in, 323–325 operations, 316–319 proper subset, 315 subset, 315 union, 317 universal, 316 Venn diagrams, 316–319 Shadow price, 191–194 Simple depreciation, 30 Simple interest, 258 Simplex method See Linear programming Simplex tableau, 206 Singular matrix, 128 Sinking fund, 291 Slack variables, 202 Slope, 10 Slope-intercept form, 15 Solution set of a system of linear inequalities, 159 bounded, 160 unbounded, 160 Square matrix, 102 Standard deviation, 443 Standard linear programming problem, 202 Standard normal curve, 464 Standard normal variable, 464 Standard viewing window, 23 Steady-state distribution vector, 495 Steady-state matrix, 496 Stochastic matrix, 486 Stochastic process, 393, 484 Straight line depreciation, 30–31 Strategies See Game theory Strictly determined game, 516 Subset, 315 Supply curve, 32 Supply equation, 32 Supply function, 32 Switching networks, 558 Symbolic logic, 537 Systems of linear equations, 68–72 dependent, 70 equivalent, 76 Gauss–Jordan elimination method, 75–85, 91–96 inconsistent, 70 solution by inverses, 132–134 612 INDEX Systems of linear equations (continued) solution by substitution, 69 three variables, 71 two variables, 68 Systems of linear inequalities, 156–157 half-planes, 156 procedure for graphing, 158 Total cost function, 30 Total output matrix, 142 Transition matrix, 486 Transitional probabilities, 485 Transportation problem, 166–167 Transpose of a matrix, 105 Tree diagram, 330, 339, 356–358, 393–395 Truth tables, 542–544 Two-person game, 512–518 Unbounded solution set, 160 Uniform sample space, 364 Union of two events, 355 Union of sets, 317 Unit column, 80 Universal set, 316 Value of a game, 517 Variable(s) basic, 203 dependent, 28 independent, 28 nonbasic, 203 random, 418 slack, 202 Variable costs, 31 Variance, 441, 457 Venn diagrams, 316–319, 355–356 Warehouse problem, 167–168, 231–233 Whole numbers, 564 Zero matrix, 105 Zero-sum game, 512 This page intentionally left blank How-To Technology Index 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Page Graph a straight line 23 Evaluate a function 37 Find the point(s) of intersection of two graphs 49 Find an equation of a least-squares line 60 Solve a system of linear equations using the Gauss–Jordan method 89, 100 Perform matrix operations 110 Perform matrix multiplication 125 Find the inverse of a square matrix 139 Analyze a Leontief input–output model 149 Use the simplex method to solve a maximization linear programming problem 222 Use the simplex method to solve a minimization linear programming problem 237 Use the simplex method to perform sensitivity analysis 239 Find the accumulated amount of an investment 273 Find the effective rate of interest 273 Find the present value of an investment 273 Find the future value of an annuity 284 Find the present value of an annuity 285 Find the payment needed to amortize a loan 297 Find the payment needed for a sinking fund 298 Evaluate n!, P(n, r), and C(n, r) 348 Simulate an experiment 363 Graph a histogram for a given set of data 425 Find the mean and standard deviation of a random variable 451 Calculate the area under the standard normal curve 466 Find the distribution vector for a Markov chain 493 Find the long-term distribution vector for a Markov chain 503 List of Applications BUSINESS AND ECONOMICS Access to capital, 449 Adjustable-rate mortgage, 291, 296 Advertising, 54, 58, 168, 170, 179, 182, 220 Agriculture, 59, 73, 87, 137, 169, 182, 236, 346, 460, 531, 534 Airline safety, 370 Allocation of funds, 169, 181, 252 Allocation of services, 488, 499 Alternative energy sources, 379 Annuities, 278, 280, 281, 283 Assembly-time studies, 361, 380, 413 Asset allocation, 169, 170, 181, 219, 220 ATM cards, 334 Auditing tax returns, 399 Authentication technology, 59 Automobile colors, 334 Automobile financing, 315 Automobile leasing, 280, 283 Automobile surveys, 534 Average rent, 448 Balloon payment mortgage, 296, 316 Banking, 58, 109 Beverage research, 409 Bidding for contracts, 346 Bidding for rights, 518 Bookstore inventories, 109 Box-office receipts, 74, 88, 122 Brand selection, 387 Break-even analysis, 41, 42, 43, 46, 47, 51, 65 Bridge loans, 270 Broadband Internet households, 35 Broadband versus dial-up, 47 Business travel expenses, 88 Buying trends of home buyers, 501 Cable television, 438 Calling cards, 57 Capital expenditures, 133, 295, 311 CDs, 267, 269, 310 City planning, 487, 488 COLAs, 307 Common stock transactions, 114, 120, 121, 153, 272, 360, 484 Company sales, 65, 302, 304, 310 Competitive strategies, 519, 520, 535 Computer-aided court transcription, 509 Consolidation of business loans, 271 Consumption functions, 34 Corn used in U.S ethanol production, 367 Corporate bonds, 270 Cost of drilling, 307 Cost of laying cable, 4, Credit cards, 311, 351 Cruise ship bookings, 478 Customer service, 361, 460 Customer surveys, 414, 425 Decision analysis, 42, 43, 47 Demand for electricity, 61, 62 Depreciation of equipment, 30, 305 Dial-up Internet households, 35 Digital TV services, 22 Digital versus film cameras, 47 Double-declining balance depreciation, 305, 308 Downloading music, 379 Durable goods orders, 367 Economic surveys, 328 Effect of inflation on salaries, 271 Electricity consumption, 61, 62, 270 Electricity generation, 379 Employee education and income, 401 Energy consumption, 63 Equilibrium quantity and price, 44, 45, 46, 48, 51, 66 Expected auto sales, 438 Expected demand, 437 Expected home sales, 438 Expected product reliability, 437 Expected profit, 430, 438 Expected sales, 437, 481 401K retirement plans, 122, 328, 378, 379 Factory workers’ wages, 477 Fighting inflation, 367, 414 Financial analysis, 199, 294, 520 Financial planning, 284, 295, 311 Financing a car, 280, 294, 295 Financing a home, 288, 294, 295, 296, 297 Flex-time, 414 Foreign exchange, 122 Gasoline consumption, 510 Gasoline sales, 107, 113, 153 Gross national product, 328 Health-care plan options, 334 Home affordability, 290, 448 Home equity, 289 Home mortgages, 288, 294, 311 Home refinancing, 296 Home sales, 113 Hours worked in some countries, 449 Housing appreciation, 370 Housing loans, 400 Income distributions, 404, 413 Industrial accidents, 445, 478 Inflation rates, 271 Information security software sales, 57 Input–output analysis, 142, 144, 145, 146, 147, 148, 149 Installment loans, 283, 310 Insurance claims, 109 Insurance probabilities, 409, 437 Interest rate prediction, 437 Inventory control and planning, 102, 109, 437 Investment analysis, 256, 281, 283, 284, 296, 438, 447 Investment clubs, 74, 88, 137 Investment options, 267, 271, 332, 343 Investment planning, 74, 183, 271 Investment portfolios, 109, 153 Investment strategies, 528, 531 Investments 74, 87, 88, 98, 121, 153, 169, 170, 181, 219, 220, 252, 271, 328, 351, 378 IRA assets, 57 IRAs, 57, 267, 281, 283, 295 LCDs versus CRTs, 47 Leasing, 47, 51 Life insurance premiums, 438 Linear depreciation, 30, 34, 65 Loan amortization, 294, 297 Loan delinquencies, 478 Machine scheduling, 153 Mail delivered, 449 Mail-order sales, 461 Management decisions, 74, 88, 98, 340, 345, 346, 520 Market equilibrium, 44, 45, 48, 66 Market for cholesterol-reducing drugs, 37, 38 Market research, 56, 183 Market share, 110, 490, 492, 500, 502, 520 Marketing surveys, 325 Maximizing production, 164, 535 Maximizing profit, 164, 168, 169, 170, 171, 175, 181, 182, 183, 187, 195, 196, 197, 199, 214, 217, 219, 220, 248, 252, 256 Microwave ownership, 459 Minimizing mining costs, 169, 182, 196, 256 Minimizing shipping costs, 7, 167, 170, 171, 182, 199, 236, 253 Money market mutual funds, 272 Money market rates, 424 Mortgages, 288, 291, 294, 296, 297 Motorcycle sales, 110 Movie attendance, 357, 367 Municipal bonds, 270 Music venues, 370 Mutual funds, 270, 272, 310 Net-connected computers in Europe, 63 Newspaper subscriptions, 329 Nuclear plant utilization, 21 Nurses’ salaries, 66 Occupancy rate, 448 Online banking, 58 Online retail sales, 271 Online sales of used autos, 58 Online spending, 57 Online travel, 63 Operations management consulting spending, 59 Optimizing production schedules, 170, 171, 219, 220, 248 Organizing production data, 108, 110, 123 Organizing sales data, 101, 111 Packaging, 443, 471 PC growth, 57 Pension funds, 270 Pensions, 271 Personal loans, 316 Personnel selection, 346, 386, 409 Petroleum production, 153 Plans to keep cars, 379 Predicting sales figures, 22 Predicting the value of art, 16 Prefab housing, 171, 220 Pricing, 136, 535 Probability of engine failure, 461 Product reliability, 399, 401, 408, 419, 450, 477 Product safety, 368 Production planning, 102, 106, 118, 123, 124, 214, 248, Production scheduling, 70, 84, 88, 98, 168, 169, 170, 171, 181, 182, 183, 196, 197, 199, 219, 248, 252 Profit functions, 31, 34, 65, 187 Promissory notes, 271 Purchasing power, 271 (continued) List of Applications (continued) Quality control, 345, 352, 360, 361, 367, 369, 373, 383, 386, 394, 397, 400, 401, 404, 408, 412, 413, 414, 450, 457, 459, 461, 475, 478, 481 Rate comparisons, 271 Rate of return on an investment, 268, 272, 310 Real estate, 74, 87, 122, 266, 271 Real estate transactions, 122, 376, 436, 438 Recycling, 350 Refinancing a home, 296, 297, 316 Reliability of a home theater system, 401 Reliability of security systems, 401 Retail sales, 378 Retirement benefits versus salary, 370 Retirement planning, 122, 283, 293, 295 Revenue growth of a home theater business, 271 Revenue of Moody’s corporation, 58 Revenue projection, 438 Robot reliability, 461 Royalty income, 282 Salary comparisons, 307 Sales growth, 22, 306, 307 Sales of drugs, 57 Sales of GPS equipment, 21, 58 Sales of navigation systems, 21 Sales of plasma TV sets, 414 Sales projections, 460 Sales tax, 34 Sampling, 345, 352, 481 Security breaches, 370 Shadow prices, 192 Shoplifting, 369 Shuttle bus usage, 361 Sinking fund, 292, 295, 298, 299 Social Security benefits, 34 Social Security contributions, 21 Social Security wage base, 58 Spending methods, 369 Staffing, 335 Starbucks’ annual sales, 63 Starbucks’ store count, 56 Starting salaries, 450 Stock transactions, 114, 120, 121, 153 Sum-of-the-years-digits method of depreciation, 307, 308 Supply and demand, 33, 35, 36, 44, 45, 48 Switching jobs, 379 Tax planning, 281, 284, 295, 310 Tax preparation, 378 Tax-deferred annuity, 281 Taxicab movement, 488, 492, 499 Telemarketing, 478 Television commercials, 220 Television pilots, 424 Television programming, 345 Testing new products, 358, 364, 366 Theater bookings, 478 Ticket revenue, 136 Tour revenue, 135 Transportation problem, 166, 182 Transportation, 169, 182, 196 Trust funds, 259, 270, 295, 308 TV households, 377 TVs in the home, 449 Unemployment rates, 437 Union bargaining issues, 334 U.S drug sales, 57 U.S financial transactions, 47 U.S health-care expenditures, 29, 55 U.S online banking households, 58 U.S online travel revenue, 63 U.S outdoor advertising, 58 Violations of the building code, 460 Volkswagen’s revenue, 481 Wage rates, 439 Waiting lines, 345, 420, 424, 428 Warehouse problem, 167, 171, 199, 231 Warranties, 375, 477 Waste generation, 63 Women’s apparel, 379 Worldwide consulting spending, 58 Zero coupon bonds, 267, 271, 272 SOCIAL SCIENCES Accident prevention, 366 Age distribution in a town, 452 Age distribution of renters, 408 Americans without health insurance, 449 Arrival times, 331, 368 Auto-accident rates, 409, 437 Birthrates, 447 Boston homicides, 448 Campaign strategies, 531 Car theft, 400 Charities, 126 Civil service exams, 477 College admissions, 21, 56, 66, 123, 400, 414, 472 College graduates, 461 College majors, 410, 492 Committee selection, 341 Commuter options, 334 Commuting times, 414 Commuter trends, 327, 492, 501 Compliance with seat belt laws, 407 Consumer decisions, 7, 270, 307, 313, 413 Consumer surveys, 324, 327, 328, 367, 378 Correctional supervision, 368 Course enrollments, 378 Court judgment, 270 Crime, 327, 408 Disposition of criminal cases, 369 Distracted driving, 380 Distribution of families by size, 424 Drivers’ tests, 346, 387 Driving age requirements, 447 Education, 477 Education and income, 401 Educational level of mothers and daughters, 494 Educational level of voters, 400 Elections, 351, 410, 450 Enrollment planning, 21, 123, 378, 400, 511 Exam scores, 439, 448, 461 Financing a college education, 271, 295 Gender gap, 409 Grade distributions, 367, 477 Green companies, 369 Gun-control laws, 380 Highway speeds, 477 Homebuying trends, 501 Homeowners’ choice of energy, 492, 501 Hours worked in some countries, 449 IQs, 477 Investment portfolios, 109 Jury selection, 346 Library usage, 422 Life expectancy, 58, 66, 110 Male life expectancy at 60, 58 Marital status of men, 449 Marital status of women, 481 Mass-transit subsidies, 57 Mortality rates, 110 Narrowing gender gap, 21 Network news viewership, 501 On-time arrivals, 481 One-and two-income families, 501 Opinion polls, 367, 408, 414, 415 Organizing educational data, 123, 322 Organizing sociological data, 425, 447, 449 Parental influence, 369 Political polls, 334, 361, 369, 491 Politics, 122, 407 Professional women, 501 Psychology experiments, 334, 491, 500 Public housing, 386 Research funding, 137 Restaurant violations of the health code, 460 Retirement expectations, 414 Retirement needs, 407 Ridership, 74, 87 Risk of an airplane crash, 380 Rollover deaths, 378 Same-sex marriage, 368 SAT scores, 56, 328, 372 Seat-belt compliance, 407 Selection of Senate committees, 341 Selection of Supreme Court judges, 409 Small-town revival, 491 Smoking and education, 411 Social ladder, 410 Social programs planning, 170, 182 Solar energy, 457, 492 Staying in touch, 369 Student dropout rate, 328 Student enrollment, 400 Student financial aid, 401 Student loans, 295 Student reading habits, 328 Student surveys, 328, 351 Study groups, 345 Switching Internet service providers (ISPs), 401 Teacher attitudes, 378 Teaching assistantships, 346 Television-viewing polls, 183, 334 Traffic surveys, 368, 480 Traffic-flow analysis, 95, 98, 99 Transcription of court proceedings, 509 Trends in auto ownership, 502, 534 U.N Security Council voting, 343 U.N voting, 346 U.S population by age, 424 Urbanization of farmland, 534 Urban–suburban population flow, 487, 488, 492 Use of public transportation, 74, 87, 492, 501 Voter affiliation, 122 Voter turnout by income, 410 Voter turnout by profession, 410 Voters, 460 Voting patterns, 409 Voting quorums, 347 Water supply, 169 Women in the professions, 501 World energy consumption, 63 LIFE SCIENCES Animal nutrition, 183, 252 Bacteria growth, 308 Birth weights of infants, 471 Birthrates, 447 Blood tests, 407 Blood types, 367, 461 Cholesterol levels, 37, 39, 108, 476 Clark’s rule, 65 Color blindness, 390 Corrective lens use, 368 Cost of hospital care, 270 Cowling’s rule, 34 Cricket chirping and temperature, 35 Crop planning 169, 182, 196, 219, 252 Dietary planning, 74, 88, 124, 136, 170, 182, 236, 252 Drug dosages, 34, 65 Drug effectiveness, 481 Drug testing, 461, 478 Female life expectancy at 65, 66 Fertilizer mixtures, 74, 87, 137 Genetics, 502, 508, 511 Heart transplant survival rate, 475 Heights of women, 452, 481 Ideal heights and weights for women, 21 Medical diagnoses, 411 Medical records, 477 Medical research, 401, 409 Medical surveys, 396 Nutrition, 98, 136, 165, 170, 176, 182, 236, 252 Obesity in children, 410 Organizing medical data, 108 Outpatient visits, 63 Probability of transplant rejection, 401 Reliability of medical tests, 408, 409 Serum cholesterol levels, 476 Smoking and emphysema, 396 Success of heart transplants, 458 Veterinary science, 183, 252 Violations of the health code, 460 Weight of whales, GENERAL INTEREST Automobile options, 319 Automobile selection, 351 Birthday problem, 384, 388 Blackjack, 334, 387 Car pools, 345 Code words, 334 Commuter train arrival times, 368 Computer dating, 334 Computing phone bills, 123 Exercise program, 307 Family food expenditure, 270 Gambler’s ruin, 506, 507 Game shows, 360 Highway speeds, 477 License plate numbers, 334 Lightning deaths, 368 Lotteries, 283, 335, 387, 437 Manned bomber research, 406 Menu selection, 351 Meteorology, 367 Poker, 342, 346, 347, 351, 352, 377, 387 Raffles, 336, 431 Roulette, 369, 387, 431, 433, 439 Saving for a college education, 280, 310 Slot machines, 335, 387, 434 Sports 327, 346, 347, 361, 439, 460, 481 Sweepstakes, 369, 460, 478 Team selection, 351, 352 Temperature conversion, 20, 35 Travel options, 333 Vacation costs, 88 Wardrobe selection, 334 Zodiac signs, 388 ... EDITION FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES This page intentionally left blank EDITION FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES S T TAN STONEHILL... fact, they can keep on trying until they get it right If students need step-by-step help, they can use the CengageNOW Tutorials that are keyed to the text and work out similar problems at their... Edition, attempts to illustrate this point with its applied approach to mathematics Our objective for this Ninth Edition is threefold: (1) to write an applied text that motivates students while