1.INTRODUCTORY MATHEMATICALINTRODUCTORY MATHEMATICAL ANALYSISANALYSISFor Business, Economics, and the Life and Social Sciences 2007 Pearson Education Asia Chapter 7Chapter 7 Linear ProgrammingLinear Programming

2. 2007 Pearson Education Asia INTRODUCTORY MATHEMATICAL ANALYSIS 0. Review of Algebra 1. Applications and More Algebra 2. Functions and Graphs 3. Lines, Parabolas, and Systems 4. Exponential and Logarithmic Functions 5. Mathematics of Finance 6. Matrix Algebra 7. Linear Programming 8. Introduction to Probability and Statistics 3. 2007 Pearson Education Asia 9. Additional Topics in Probability 10. Limits and Continuity 11. Differentiation 12. Additional Differentiation Topics 13. Curve Sketching 14. Integration 15. Methods and Applications of Integration 16. Continuous Random Variables 17. Multivariable Calculus INTRODUCTORY MATHEMATICAL ANALYSIS 4. 2007 Pearson Education Asia To represent geometrically a linear inequality in two variables. To state a linear programming problem and solve it geometrically. To consider situations in which a linear programming problem exists. To introduce the simplex method. To solve problems using the simplex method. To introduce use of artificial variables. To learn alteration of objective function. To define the dual of a linear programming problem. Chapter 7: Linear Programming Chapter ObjectivesChapter Objectives 5. 2007 Pearson Education Asia Linear Inequalities in Two Variables Linear Programming Multiple Optimum Solutions The Simplex Method Degeneracy, Unbounded Solutions, and Multiple Solutio Artificial Variables Minimization The Dual 7.1) 7.2) 7.3) 7.4) Chapter 7: Linear Programming Chapter OutlineChapter Outline 7.5) 7.6) 7.7) 7.8) 6. 2007 Pearson Education Asia Chapter 7: Linear Programming 7.1 Linear Inequalities in 2 Variables7.1 Linear Inequalities in 2 Variables Linear inequality is written as where a, b, c = constants and not both a and b are zero. 0 or0 or0 or0 ++ >++ ++