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Linear Programming History (background)

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Leigh Buist

on 28 January 2013

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Transcript of Linear Programming History (background)

The history of Linear Programming Linear programming is one of the
main applications of mathematics
used in business and the social sciences.
The process known as linear programming
is used to find minimum cost, maximum profit,
the maximum amount of learning that can take
place under given conditions, and so on. The
procedures for solving linear programming
problems were developed in 1947 by George
Dantzig, while working on the problem of
allocating supplies for Air Force troops during
World War II, in a way that minimized total
cost. Today, business and industry are
quick to use Dantzig's methods when
solving problems related to warehouse
locations, factory designs, and utilizing
resources among many
other problems. History Vocabulary The inequalities limiting the
problem at hand. A function in two variables f(x,y)
that is the objective to maximize
or minimize, such as profit, etc. Constraints Feasible Region The shaded polygonal area created
by the intersection of the graphs
of inequalities. It is the
location where every
constraint is met or satisfied. Unbounded A function where no maximum
value exists. The shaded regions
of the constraints do not
form a closed figure. Objective Quantity 5.Determine the maximum
(highest value) and the
minimum (lowest value)
by using substitution. 1.Graph each inequality on a
coordinate axes system. 2.Find the feasible region by
shading correctly. 3.Determine the vertices of
the feasible region
(polygon) that are
formed. 4.Evaluate each coordinate
in the objective
quantity. Procedure The Widget Manufacturing company makes two products, Alpha Widgets and Beta Widgets. Each Alpha Widget gives a profit of $3, while each Beta Widget earns $7. The company must manufacture at least one Alpha Widget per day to satisfy its customers, but no more than five because of the number of employees needed to create the item. Also, the number of Beta Widgets produced cannot exceed six per day. As a further constraint, Alpha Widgets cannot exceed the number of Beta Widgets. Example Problem
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