**Linear programming** is a technique to get the best outcome (for example maximum profit or minimum cost) in a mathematical model whose requirements are shown by linear relationships.

Linear programming (LP) is actually a special case of mathematical optimization.

The word **'linear' means** that the relationships are represented by straight
lines, i.e., the relationships are of the form *k = p + qx*. In
other words, it is used to describe the relationships among two or more
variables, which are directly proportional. The word **'programming' means** the optimal allocation of limited resources.

In fact, every organization faces the problem of allocating limited
resources to different activities. Such type of problem arises when
there are alternative ways of performing a number of activities. For
instance, consider a manufacturing firm where it is possible to manufacture
a variety of products. Each of the products has a certain margin of
profit per unit. These products use a common pool of resources whose
availability is limited. Now the problem is to carefully allocate these
resources to different types of finished products in such a way so that
the total return may be maximum. In such a situation, the management's
decision may be based on past experience and intuition, but decision
so made is subjective rather than objective.

"Telling the future by looking at the past assumes that conditions remain constant. This is like driving a car by looking in the rearview mirror." -Herb Brody

## Definition of Linear Programming

Linear Programming (LP) is a versatile technique for assigning a fixed amount of resources among competing factors, in such a way that some objective is optimized and other defined conditions are also satisfied.

Linear programming is a mathematical technique for determining the optimal allocation of resources and obtaining a particular objective when there are alternative uses of the resources. The objective may be cost minimization or inversely profit maximization.

*Linear programming* has been successfully applied to a variety of problems
of management, such as production, advertising, transportation, refinery
operation, investment analysis, etc. Over the years, linear programming
has been found useful not only in business and industry but also in
non-profit organizations such as government, hospitals, libraries, education,
etc. Actually, linear programming improves the quality of decisions
by amplifying the analytic abilities of a decision maker.

Please note
that the result of the mathematical models that you will study cannot
substitute for the decision maker's experience and intuition,
but they provide the comprehensive data needed to apply his knowledge
effectively.

"Experience is a comb which nature gives to men when they are bald." -Anonymous