Abstract
This chapter discusses the basic ideas and techniques of linear programming. This area of applied mathematics was developed in the late 1940s to solve a number of resource allocation problems for the federal government. It has become an essential tool in operations research and has been applied to a remarkably varied number of real problems with enormous savings in money and resources. The chapter presents a general algebraic technique for the solution of the linear programming problem. A linear programming problem in canonical form is solved by finding all the basic solutions, discarding those which are not feasible, and finding an optimal solution among the remaining. The chapter also illustrates the method of a simplex algorithm. The simplex algorithm consists of two steps: (1) a way of finding out whether a given basic feasible solution is an optimal solution, and (2) a way of obtaining an adjacent basic feasible solution with a larger value for the objective function.
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