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# Linear Programming

Linear programming is a way to determine the best outcome in a given mathematical model for some list of requirements represented as linear relationships. Linear programming is specific case of mathematical programming. Linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. A linear programming algorithm finds a point in the polyhedron where this function has the smallest value if such point exists.

Linear programming can be applied to various fields of study. It is used in business and economics but is also utilized in engineering applications. Some industries that utilize linear programming models include transportation energy telecommunications and manufacturing. Many practical problems in operation research can be expressed as linear programming problems.

Standard form is the typical form of describing a linear programming problem. This form consists of three parts that are shown below:

A linear function to be maximized

F(x1, x2) = c1x1 + c2x2

Problem constraints

A11x1 + a12x2 <= b1

A21x1 + a22x2 <= b2

A31x1 + a32x2 <= b3

Non negative variables

X1>= 0

X2>= 0

The problem is usually expressed in matrix form and therefor becomes:

Ma{cTx| Ax <= b ^ x >= 0}

## BrainMass Categories within Linear Programming

### Optimization

Solutions: 406

Optimization is the selection of a best element from some set of available alternatives.

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### Linear Programming Using the M-technique

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### LP Scheduling problem

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### Integer Programming - Linear Programming

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### Solving Linear Programming in Excel Solver-Maximization

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### Integer Programming Problem: Transportation and Transshipment

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### Applications of Linear Programming

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### Linear Programs and Inequalities

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### The solution gives detailed steps on creating your own linear programming problem: how to make objective function, how to set up constraints. Finally, all functions and equations are shown.

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