Chapter 1 Linear Equations 1
1.1 Lines 2
1.2 Pairs of Lines 22
1.3 Applications in Business and Economics 30
1.4 Scatter Diagrams; Linear Curve Fitting 35
Chapter Review 42
Chapter Project 45
Chapter 2 Systems of Linear Equations 49
2.1 Systems of Linear Equations: Substitution; Elimination 50
2.2 Systems of Linear Equations: Gaussian Elimination 69
2.3 Systems of m Linear Equations Containing n Variables 88
Chapter Review 98
Chapter Project 101
Chapter 3 Matrices 103
3.1 Matrix Algebra 104
3.2 Multiplication of Matrices 121
3.3 The Inverse of a Matrix 135
3.4 Applications in Economics (the Leontief Model), Accounting, and Statistics (the Method of Least Squares) 152
Chapter Review 170
Chapter Project 172
Chapter 4 Linear Programming with Two Variables 175
4.1 Systems of Linear Inequalities 176
4.2 A Geometric Approach to Linear Programming Problems with Two Variables 191
4.3 Models Utilizing Linear Programming with Two Variables 199
Chapter Review 209
Chapter Project 213
Chapter 5 Linear Programming: Simplex Method 217
5.1 The Simplex Tableau; Pivoting 218
5.2 The Simplex Method: Solving Maximum Problems in Standard Form 236
5.3 Solving Minimum Problems Using the Duality Principle 257
5.4 The Simplex Method for Problems Not in Standard Form 269
Chapter Review 284
Chapter Project 289
Chapter 6 Finance 293
6.1 Interest 294
6.2 Compound Interest 301
6.3 Annuities; Sinking Funds 316
6.4 Present Value of an Annuity; Amortization 329
6.5 Annuities and Amortization Using Recursive Sequences 345
Chapter Review 349
Chapter Project 352
Chapter 7 Probability 355
7.1 Sets 356
7.2 The Number of Elements in a Set 365
7.3 The Multiplication Principle 373
7.4 Sample Spaces and the Assignment of Probabilities 378
7.5 Properties of the Probability of an Event 391
7.6 Expected Value 403
Chapter Review 412
Chapter Project 417
Chapter 8 Additional Probability Topics 421
8.1 Conditional Probability 422
8.2 Independent Events 433
8.3 Bayes’ Theorem 445
8.4 Permutations 457
8.5 Combinations 465
8.6 The Binomial Probability Model 480
Chapter Review 496
Chapter Project 501
Chapter 9 Statistics 505
9.1 Introduction to Statistics: Data and Sampling 506
9.2 Representing Qualitative Data Graphically: Bar Graphs; Pie Charts 509
9.3 Organizing and Displaying Quantitative Data 517
9.4 Measures of Central Tendency 532
9.5 Measures of Dispersion 541
9.6 The Normal Distribution 553
Chapter Review 565
Chapter Project 572
Chapter 10 Markov Chains; Games 575
10.1 Markov Chains and Transition Matrices 576
10.2 Regular Markov Chains 587
10.3 Absorbing Markov Chains 600
10.4 Two-Person Games 611
10.5 Mixed Strategies 615
10.6 Optimal Strategy in Two-Person Zero-Sum Games with 2 x 2 Matrices 620
Chapter Review 627
Chapter Project 631
Chapter 11 Logic 633
11.1 Propositions 634
11.2 Truth Tables 639
11.3 Implications; The Biconditional Connective; Tautologies 648
11.4 Arguments 655
11.5 Logic Circuits 661
Chapter Review 665
Chapter Project 668
Appendix A Review A-1
A.1 Real Numbers A-1
A.2 Algebra Essentials A-16
A.3 Exponents and Logarithms A-28
A.4 Recursively Defined Sequences: Geometric Sequences A-34
A.5 The Binomial Theorem A-42
Appendix B Using Lindo to Solve Linear Programming Problems B-1
Appendix C Graphing Utilities C-1
C.1 The Viewing Rectangle C–1
C.2 Using a Graphing Utility to Graph Equations C–3
C.3 Square Screens C–6
C.4 Using a Graphing Utility to Graph Inequalities C–7
Answers to Odd-Numbered Problems AN-1
Photo Credits PC-1
Subject Index I-1
