# Linear programming

Reference work entry

First Online:

**DOI:**https://doi.org/10.1007/1-4020-0611-X_545

Linear programming is one of the most widely used techniques of operations research and management science. Its name means that planning (*programming*) is being done with a mathematical model (called a *linear programming model*) where all the functions in the model are *linear* functions.

## LINEAR PROGRAMMING MODELMODELS

Linear programming models come in a variety of forms. To illustrate one common form, consider the problem of determining the most profitable mix of products for a manufacturer. Let

*n*be the number of possible products. For each product*j*(*j*= 1, 2, ...,*n*), a*decision variable x*_{j}is introduced to represent the decision on its production rate. Let*c*_{j}be the profit per unit of product*j*produced, and let*Z*be the total rate of profit resulting from the choice of product mix. This choice is constrained by the limited capacities of the production facilities available for these products. Let*m*be the number of different types of facilities needed. For each type*i*(*i*= 1, 2, ...,*m*...This is a preview of subscription content, log in to check access.

## References

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## Copyright information

© Kluwer Academic Publishers 2001