Editing George Dantzig (section)

====Linear programming====
[[Linear programming]] is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given [[mathematical model]] for some list of requirements represented as linear relationships. Linear programming arose as a mathematical model developed during [[World War II]] to plan expenditures and returns in order to reduce costs to the army and increase losses to the enemy. It was kept secret until 1947. Postwar, many industries found its use in their daily planning.

The founders of this subject are [[Leonid Kantorovich]], a Russian mathematician who developed linear programming problems in 1939, Dantzig, who published the [[Simplex algorithm|simplex method]] in 1947, and [[John von Neumann]], who developed the theory of the [[duality (optimization)|duality]] in the same year.

Dantzig was asked to work out a method the Air Force could use to improve their planning process.<ref>{{Cite web|title=Biographical Profiles: Dantzig, George B.|url=https://www.informs.org/Explore/History-of-O.R.-Excellence/Biographical-Profiles/Dantzig-George-B|access-date=2020-10-30|website=INFORMS|language=en-US}}</ref>  This led to his original example of finding the best assignment of 70 people to 70 jobs, showing the usefulness of [[linear programming]]. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the universe. However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the Simplex algorithm. The theory behind linear programming drastically reduces the number of possible optimal solutions that must be checked.

In 1963, Dantzig's ''Linear Programming and Extensions'' was published by [[Princeton University Press]]. The book quickly became a standard text in linear programming.