LINEAR PROGRAM Meaning and
Definition
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A linear program, also known as linear programming, refers to a mathematical technique used to optimize the allocation of resources for achieving a certain objective. It involves formulating and solving mathematical models with linear objective functions and linear inequality or equality constraints. Linear programs aim to find the best possible outcome among a set of feasible solutions by maximizing or minimizing the value of a linear objective function, subject to a number of linear constraints.
In a linear program, the objective function represents the goal that needs to be maximized or minimized, such as maximizing profit or minimizing costs. The objective function is linear, meaning it can be expressed as a linear combination of variables with specified coefficients. The constraints, on the other hand, represent the limitations or restrictions on the variables. These constraints are linear inequalities or equalities that limit the values that the variables can take.
Solving a linear program involves identifying the feasible region, which is the intersection of the constraints, and searching for the optimal solution within this region that satisfies the objective function. Mathematical techniques such as the simplex algorithm or the interior-point method are commonly employed to find the optimal solution for linear programs.
Linear programming finds various applications in different fields including operations research, economics, engineering, finance, transportation, and logistics, among others. It is an essential tool for decision-making processes, as it helps in making efficient use of limited resources to achieve the desired outcome.
Etymology of LINEAR PROGRAM
The term "linear program" is derived from the combination of the words "linear" and "program".
The word "linear" originates from the Latin word "linearis", which means "related to a line". In mathematics, a linear function refers to a function that can be represented by a straight line on a graph. This term is often used to describe relationships, equations, or systems that can be expressed using a straight line.
The word "program" comes from the Greek word "programma", which means a written public notice or proclamation. Over time, it evolved to refer to a plan or schedule of activities. In computer science and mathematics, a program typically refers to a set of instructions or procedures designed to perform specific functions or solve particular problems.
Combining these two terms, "linear program" refers to a mathematical optimization problem that involves maximizing or minimizing a linear objective function under a set of linear equality and inequality constraints.
