In the Little Mathematics Library series we now come to Systems of
Linear Inequalities by A. S. Solodovnikov.
The book tells about the relation of systems of linear
inequalities to convex polyhedra, gives a description of the
set of all solutions of a system of linear inequalities,
analyses the questions of compatibility and
incompatibility; finally, it gives an insight into linear
programming as one of the topics in the theory of
systems of linear inequalities. The last section but one
gives a proof of duality theorem of lienar programming.
The book is intended for senior pupils and all amateur
The book was translated the Russian by Vladimir Shokurov and was
first published by Mir in 1979.
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1. Some Facts from Analytic Geometry 8
2. Visualization of Systems of Linear Inequalities In Two or Three Unknowns 17
3. The Convex Hull of a System of Points 22
4. A Convex Polyhedral Cone 25
5. The Feasible Region of a System of Linear Inequalities in Two Unknowns 31
6. The Feasible Region of a System in Three Unknowns 44
7. Systems of Linear Inequalities in Any Number of Unknowns 52
8. The Solution of a System of Linear Inequalities by successive Reduction of the Number of Unknowns 57
9. Incompatible Systems 64
10. A Homogeneous System of Linear Inequalities. The Fundamental Set of Solutions 69
11. The Solution of a Nonhomogeneous System of Inequalities 81
12. A Linear Programming Problem 84
13. The Simplex Method 91
14. The Duality Theorem in Linear Programming 101
15. Transportation Problem 107