Linear programming model

Linear programming model

IntroductionImage result for Linear programming model

Linear programming is a widely used mathematical modeling technique to determine the optimum allocation of scarce resources among competing demands. Resources typically include raw materials, manpower, machinery, time, money and space. The technique is very powerful and found especially useful because of its application to many different types of real business problems in areas like finance, production, sales and distribution, personnel, marketing and many more areas of management. As its name implies, the linear programming model consists of linear objectives and linear constraints, which means that the variables in a model have a proportionate relationship. For example, an increase in manpower resource will result in an increase in work output.

Essentials of Linear Programming Model

1.
Limited resources
:   limited number of labour, material equipment and finance.
2.
Objective
:   refers to the aim to optimize (maximize the profits or minimize the costs).
3.
Linearity
:   increase in labour input will have a proportionate increase in output.
4.
Homogeneity
:   the products, workers’ efficiency, and machines are assumed to be identical.
5.
Divisibility
:   it is assumed that resources and products can be divided into fractions. (In case the fractions are not possible, like production of one-third of a computer, a modification of linear programming called integer programming can be used).