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1. Linear Programming - Wikipedia, The Free Encyclopedia
Linear programming (LP) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given
http://en.wikipedia.org/wiki/Linear_programming

Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search Linear programming LP ) 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 equations. More formally, linear programming is a technique for the optimization of a linear objective function , subject to linear equality and linear inequality constraints . Given a polytope and a real -valued affine function defined on this polytope, a linear programming method will find a point on the polytope where this function has the smallest (or largest) value if such point exists, by searching through the polytope vertices. Linear programs are problems that can be expressed in canonical form where x represents the vector of variables (to be determined), c and b are vectors of (known) coefficients and A is a (known) matrix of coefficients. The expression to be maximized or minimized is called the objective function c T x in this case). The equations

2. Hilbert Basis (linear Programming) - Wikipedia, The Free Encyclopedia
In linear programming, a Hilbert basis for a convex cone is an integer cone
http://en.wikipedia.org/wiki/Hilbert_basis_(linear_programming)

Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search In linear programming , a Hilbert basis for a convex cone is an integer cone basis : minimal set of integer vectors such that every integer vector in the convex cone is a linear combination of the vectors in the Hilbert basis with non-negative integer coefficients. More precisely, a set of integer vectors is a Hilbert basis if every integer vector in its convex cone is also in its integer cone Bruns, Winfried; Gubeladze, Joseph; Henk, Martin; Martin, Alexander; Weismantel, Robert (1999), "A counterexample to an integer analogue of Carathéodory's theorem", Journal für die reine und angewandte Mathematik doi 10.1515/crll.1999.045 Cook, William John; Fonlupt, Jean; Schrijver, Alexander (1986), "An integer analogue of Carathéodory's theorem", Journal of Combinatorial Theory. Series B doi 10.1016/0095-8956(86)90064-X Eisenbrand, Friedrich; Shmonin, Gennady (2006), "Carathéodory bounds for integer cones", Operations Research Letters doi 10.1016/j.orl.2005.09.008

3. Linear Programming : Good Math, Bad Math
May 7, 2008 In my last post on game theory, I said that you could find an optimal probabilistic grand strategy for any twoplayer, simultaneous move,
http://scienceblogs.com/goodmath/2008/05/linear_programming.php

4. Linear Programming Summary And Analysis Summary | BookRags.com
Linear programming summary with 19 pages of lesson plans, quotes, chapter summaries, analysis, encyclopedia entries, essays, research information, and more.
http://www.bookrags.com/Linear_programming

5. Linear Programming — Sage Constructions V4.5.3
Linear programming is very useful in many optimization and graphtheoretic problems because of its wide range of expression. A linear program can be written
http://www.sagemath.org/doc/constructions/linear_programming.html

Extractions: A linear program consists of the following two pieces of information: A linear program solver would then try to find a solution to the system of constraints such that the objective function is optimized, and return specific values for the variables. A mixed integer linear program is a linear program such that some variables are forced to take integer values instead of real values. This difference affects the time required to solve a particular linear program. Indeed, solving a linear program can be done in polynomial time while solving a general mixed integer linear program is usually -complete, i.e. it can take exponential time, according to a widely-held belief that Linear programming is very useful in many optimization and graph-theoretic problems because of its wide range of expression. A linear program can be written to solve a problem whose solution could be obtained within reasonable time using the wealth of heuristics already contained in linear program solvers. It is often difficult to theoretically determine the execution time of a linear program, though it could produce very interesting results in practice. For more information, consult the Wikipedia page dedicated to linear programming:

6. Linear Programming
A linear program is a mathematical optimization model that has a linear objective function and a set of linear constraints. To provide a quick overview, we describe below what
http://www.utdallas.edu/~scniu/OPRE-6201/documents/LP1-Linear_Programming.html

Extractions: Linear Programming A linear program is a mathematical optimization model that has a linear objective function and a set of linear constraints. To provide a quick overview, we describe below what is known as the product-mix problem. The Product-Mix Problem A company manufactures two models of a product, which we call the regular model and the enhanced model. Two resources, A and B, are needed for the manufacturing of units of this product; and the detailed resource requirements are given in the following table: This means, for example, 3 units of Resource A and 2 units of Resource B are consumed in the manufacturing of each unit of the regular model. The resources could represent hours of labor, amounts of raw material, available electrical power, and so on. Suppose further that the company has 650 units of Resource A and 500 units of Resource B available per week, and that the net profits for selling units of the regular model and the enhanced model are given respectively as \$5 and \$7 per unit. The question of interest is: What are the optimal weekly production levels for these two models? To formulate this problem, we first define a set of decision variables. Let

7. Linear Programming: Facts, Discussion Forum, And Encyclopedia Article
Linear programming (LP) 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
http://www.absoluteastronomy.com/topics/Linear_programming

Extractions: Home Discussion Topics Dictionary ... Login Linear programming Overview Linear programming (LP) 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 Mathematical model A mathematical model uses mathematical language to describe a system. The process of developing a mathematical model is termed mathematical modelling...

8. Linear Programming - Definition
In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear.
http://www.wordiq.com/definition/Linear_programming

Extractions: In mathematics, linear programming (LP) problems are optimization problems in which the objective function and the constraints are all linear Linear programming is an important field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP 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. Contents showTocToggle("show","hide") 1 Example

9. Linear Programming Technique-Definition, Example And Problem Solution
Linear programming is a mathematical technique which permits determination of the best use of available resources. To give example the application of linear
http://www.accountingformanagement.com/linear_programming.htm

Extractions: www.accountingforum.org . We love to work for you! Linear programming is a mathematical technique which permits determination of the best use of available resources. It is a valuable aid to management because it provides a systematic and efficient procedure which can be used as a guide in decision making. The heart of management's responsibility is the best or optimum use of limited resources that include money, personnel, materials, facilities, and time. Linear Programming-Maximization of Contribution Margin-Graphical Method The contribution margin is one measure of whether management is making the best use of resources. When the total contribution margin is maximized, management's profit objective should be satisfied. Click here to read full article Linear Programming-Maximization of Contribution Margin-Simplex Method Simplex method is considered one of the basic techniques from which many linear programming techniques are directly or indirectly derived. The

10. Operations Research/Linear Programming - Wikibooks, Collection Of Open-content T
May 31, 2010 Linear Programming (LP) is a mathematical modelling technique useful for allocation of limited resources such as material, machines etc to
http://en.wikibooks.org/wiki/Operations_Research/Linear_Programming

Extractions: From Wikibooks, the open-content textbooks collection Operations Research This page may need to be reviewed for quality. Jump to: navigation search Linear Programming (LP) is a mathematical modelling technique useful for allocation of limited resources such as material, machines etc to several competing activities such as projects, services etc. A typical linear programming problem consists of a linear objective function which is to be maximized or minimized subject to a finite number of linear constraints. (By a linear function we mean a function of the form where are all variables.) The founders of LP are George B. Dantzig, who published the simplex method in 1947, John von Neumann, who developed the theory of the duality in the same year, and Leonid Kantorovich, a Russian mathematician who used similar techniques in economics before Dantzig and won the Nobel prize in 1975 in economics. The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger major theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior point method for solving linear programming problems. Two variable LP models don't usually exist in practice but their study can provide us with an example as to how a general model can be handled.

11. Linear Programming - NEOS
Feb 25, 2007 Software for linear programming (including network linear programming) consumes more computer cycles than software for all other kinds of
http://wiki.mcs.anl.gov/NEOS/index.php/Linear_Programming

Extractions: Jump to: navigation search Software for linear programming (including network linear programming) consumes more computer cycles than software for all other kinds of optimization problems combined . There is a proliferation of linear programming software with widely varying capabilities and user interfaces. The most recent survey of linear programming software for desktop computers carried out by OR/MS Today (19 (1992), pp. 44-59) gave details o n 49 packages! The basic problem of linear programming is to minimize a linear objective functi on of continuous real variables, subject to linear constraints. For purposes of describin g and analyzing algorithms, the problem is often stated in the standard form where x is the vector of unknowns, c is the cost vector, and A is the constraint matrix. The feasible region described by the constraints is a polytope, or simplex , and at least one member of the solution set lies at a vertex of this polytope. The simplex algorithm , so named because of the geometry of the feasible set, underlies the vast majority of available software packages for linear programming. However, this situation may change in the future, as more software for interior-point algorithms becomes available.

12. Linear Programming
File Format PDF/Adobe Acrobat Quick View
http://www.lix.polytechnique.fr/~liberti/teaching/mpri/06/linear_programming.pdf

13. School Maths: Algebra
Home. Grade 812 Maths. Algebra. Number patterns. Finance. Functions and graphs. Linear programming

14. 1 Linear Programming Linear Programming Is A Mathematical
File Format PDF/Adobe Acrobat Quick View
http://highered.mcgraw-hill.com/sites/dl/free/0073402818/459485/Linear_Programmi

15. Linear Programming Word Problems
Linear programming word problems solved step by step, optimization, linear functions, objective function, constraints, feasible solution, optimal solution,
http://www.vitutor.com/alg/linear_programming/programming_problems.html

Extractions: A company manufactures and sells two models of lamps, L1 and L2. To manufacture each lamp, the manual work involved in model L1 is 20 minutes and for L2, 30 minutes. The mechanical (machine) work involved for L1 is 20 minutes and for L2, 10 minutes. The manual work available per month is 100 hours and the machine is limited to only 80 hours per month. Knowing that the profit per unit is \$15 and \$10 for L1 and L2, respectively, determine the quantities of each lamp that should be manufactured to obtain the maximum benefit. With the start of school approaching, a store is planning on having a sale on school materials. They have 600 notebooks, 500 folders and 400 pens in stock, and they plan on packing it in two different forms. In the first package, there will be 2 notebooks, 1 folder and 2 pens, and in the second one, 3 notebooks, 1 folder and 1 pen. The price of each package will be \$6.50 and \$7.00 respectively. How many packages should they put together of each type to obtain the maximum benefit? On a chicken farm, the poultry is given a healthy diet to gain weight. The chickens have to consume a minimum of 15 units of Substance A and another 15 units of Substance B. In the market there are only two classes of compounds: Type X, with a composition of one unit of A to five units of B, and another type, Y, with a composition of five units of A to one of B. The price of Type X is \$10 and Type Y, \$30. What are the quantities of each type of compound that have to be purchased to cover the needs of the diet with a minimal cost?

16. Linear Programming FAQ - NEOS
The Linear Programming FAQ was established by John W. Gregory and is currently being maintained by Robert Fourer and the Optimization Technology Center of Argonne National
http://wiki.mcs.anl.gov/NEOS/index.php/Linear_Programming_FAQ

17. USING LINEAR PROGRAMMING TO SOLVE SYSTEMS OF EQUATIONS AND
File Format PDF/Adobe Acrobat Quick View
http://www.pstcc.edu/facstaff/jahrens/math1630/linear_programming.pdf

18. HSOR.org: What Is OR
The first modules we developed in this series focused on linear programming. The father of linear programming is George Dantzig, who developed between 1947
http://www.hsor.org/what_is_or.cfm?name=linear_programming

19. Linear Programming — Sage Constructions V4.4.4
Linear programming is very useful in many optimization and graphtheoretic problems because of its wide range of expression. A linear program can be written
http://sagemath.com/doc/constructions/linear_programming.html

Extractions: A linear program consists of the following two pieces of information: A linear program solver would then try to find a solution to the system of constraints such that the objective function is optimized, and return specific values for the variables. A mixed integer linear program is a linear program such that some variables are forced to take integer values instead of real values. This difference affects the time required to solve a particular linear program. Indeed, solving a linear program can be done in polynomial time while solving a general mixed integer linear program is usually -complete, i.e. it can take exponential time, according to a widely-held belief that Linear programming is very useful in many optimization and graph-theoretic problems because of its wide range of expression. A linear program can be written to solve a problem whose solution could be obtained within reasonable time using the wealth of heuristics already contained in linear program solvers. It is often difficult to theoretically determine the execution time of a linear program, though it could produce very interesting results in practice. For more information, consult the Wikipedia page dedicated to linear programming:

20. Mathwords: Linear Programming
Jul 29, 2008 Linear Programming. An algorithm for solving problems asking the largest or smallest possible value of a linear polynomial.
http://www.mathwords.com/l/linear_programming.htm

Extractions: Linear Programming An algorithm for solving problems asking the largest or smallest possible value of a linear polynomial . Any restrictions on the problem must be expressed as a system of inequalities ; in particular, all equations and/or inequalities must be linear. Note: The region defined by the system will always by convex

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