Abstract
This chapter introduces the basic ideas and techniques of linear programming. It elucidates various examples of linear programming problems—the activity analysis or product mix, the diet problem, the transportation problem, the blending problem, and the financial problem. The chapter also gives a mathematical model associated with these problems. It explains equalities and inequalities in a linear programming problem, and how every minimization problem can be viewed as a maximization problem and conversely. The chapter describes how to reverse an inequality; how to change equality to an inequality; and the process of scaling, which is used to make all coefficients in a linear programming problem approximately the same size. The chapter describes how to conveniently write linear programming problems in matrix notation and what are its feasible and optimal solutions. The chapter focuses on geometry of linear programming problems—the geometry of a constraint, geometry of the objective function, and geometry of the set of feasible solutions.
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