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This text is written for the business major with enough mathematical background to appreciate an occasional departure from a main emphasis on applications. The first five chapters discuss linear problems with linear programming the central topic. The necessary matrix algebra background is developed in Chapter 2. Chapters 6 and 7 require differential calculus at a level comparable to that of first year engineering and science students. The key elements of calculus needed for optimization are recalled at the beginning of Chapter 6. The eighth chapter is devoted to integer programming including branch and bound algorithms for the knapsack and traveling salesman problems and an emphasis on problem formulation. Chapter 9 is a short introduction to dynamic programming and the last chapter contains case studies at a level a little higher than the problems in the text.