17-04-2014, 03:06 PM
Linear Programming
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Introduction
In this chapter, we give an introduction to linear programming. Linear programming
(LP) is a mathematical method for finding optimal solutions to problems. It deals
with the problem of optimizing (maximizing or minimizing) a linear function, subject
to the constraints imposed by a system of linear inequalities. It is widely used in
industry and in government. Historically, linear programming was first developed
and applied in 1947 by George Dantzig, Marshall Wood, and their associates at the
U.S. department of the Air Force, the early applications of LP were thus in military
field. However, the emphasis in applications has now moved to the general industrial
area. Linear programming today is concerned with the efficient use or allocation of
limited resources to meet desired objectives.
Before formally defining a LP problem, we define the concepts of linear function
and linear inequality.