I need some reference book suitable for self-study with many solved examples and solutions preferably for exercise questions for following study. Need basic honours undergraduate level text , suitable for self study
Linear Programming: Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. Transportation and assignment problems.*
I have a background of Linear Algebra, Calculus (single and multi-variable), some real analysis and group theory. For comparison, I've read Stephen Abbott's Understanding Analysis and Fraleigh's A First Course in Abstract Algebra.
Best Answer
The Question calls for a book suitable for self-study of linear programming "with many solved examples and solutions". This topic is usually blended with others in a mathematics course, and I'm a little doubtful about what "basic honours undergraduate level text" should mean in this context.
What comes to mind as an inexpensive text targeted at self-study is Schaum's Outline Series Operations Research (2nd edition) by Bronson and Naadimuthu. After the first introductory chapter on Mathematical Programming, there follow four chapters which cover all the fundamental aspects of formulating and solving linear programs. The book boasts "310 fully solved problems" and "[h]undreds of practice problems" (whose answers are given in the final "Answers to Supplementary Problems" section), a proportional number of which are for later chapters (four on Integer Programming, three on Nonlinear Programming, etc.).
One is likely to find a new copy of this at a local bookstore for about $20 US, and more cheaply in used bookstores or online. If one were interested in pursuing a study (after this initial foray) of proofs connected to the simplex algorithm and its variants, I'd be apt to consider texts for algorithms and complexity theory. Certainly there is interesting material from late 20th century investigations, and much of this can be gleaned from online publications once the basics are mastered.