Systems of Linear Inequalities

Contents......Page 6
Preface......Page 8
1. Some Facts from Analytic Geometry......Page 9
2. Visualization of Systems of Linear Inequalities in Two or Three Unknowns......Page 18
3. The Convex Hull of a System of Points......Page 23
4. A Convex Polyhedral Cone......Page 26
5. The Feasible Region of a System of Linear Inequalities in Two Unknowns......Page 32
6. The Feasible Region of a System in Three Unknowns......Page 45
7. Systems of Linear Inequalities in Any Number of Unknowns......Page 53
8. The Solution of a System of Linear Inequalities by Successive Reduction of the Number of Unknowns......Page 58
9. Incompatible Systems......Page 65
10. A Homogeneous System of Linear Inequalities. The Fundamental Set of Solutions......Page 70
11. The Solution of a Nonhomogeneous System of Inequalities......Page 82
12. A Linear Programming Problem......Page 85
13. The Simplex Method......Page 92
14. The Duality Theorem in Linear Programming......Page 102
15. Transportation Problem......Page 108