Editing Linear programming (section)

== Uses ==
Linear programming is a widely used field of optimization for several reasons. Many practical problems in [[operations research]] can be expressed as linear programming problems.<ref name="dantzig1982"/> Certain special cases of linear programming, such as ''[[network flow problem|network flow]]'' problems and [[multi-commodity flow problem|''multicommodity flow'' problems]], are considered important enough to have much research on specialized algorithms. A number of algorithms for other types of optimization problems work by solving linear programming problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as ''duality,'' ''decomposition,'' and the importance of ''convexity'' and its generalizations. Likewise, linear programming was heavily used in the early formation of [[microeconomics]], and it is currently utilized in company management, such as planning, production, transportation, and technology. Although the modern management issues are ever-changing, most companies would like to [[profit maximization|maximize profits]] and minimize costs with limited resources. Google also uses linear programming to stabilize YouTube videos.<ref>{{cite book |author1=M. Grundmann |author2=V. Kwatra |author3=I. Essa |title=CVPR 2011 |chapter=Auto-directed video stabilization with robust L1 optimal camera paths |date=2011 |pages=225–232 |doi=10.1109/CVPR.2011.5995525 |isbn=978-1-4577-0394-2 |s2cid=17707171 |url=https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/37041.pdf |language=English}}</ref>