LINEAR PROGRAMMING Meaning and
Definition
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Linear programming is a mathematical optimization technique used to determine the best possible outcome in a given set of constraints. It involves establishing a linear relationship between a set of variables and an objective function, subject to several linear inequalities or equalities. The goal of linear programming is to maximize or minimize the objective function, while adhering to the specified constraints.
In linear programming, the variables represent the quantity of resources to be allocated to different activities, and the objective function quantifies the measure of performance to be optimized. The constraints define the limitations or restrictions on the variables, often in the form of limited resources, budget constraints, or capacity restrictions.
This technique finds application in various fields, such as manufacturing, supply chain management, finance, and transportation. It enables decision-makers to make informed choices by evaluating different alternatives within the given constraints. Linear programming is based on the assumption that the relationships between variables and constraints are linear, which simplifies the problem and allows for efficient mathematical programming.
Solving a linear programming problem usually involves graphical methods or algorithms, such as the simplex method, to identify the optimal solution. The optimal solution represents the values of the variables that maximize or minimize the objective function, while still satisfying the constraints. Sensitivity analysis is often performed to understand how changes in parameters or constraints impact the optimal solution and enable decision-makers to adapt to dynamic situations.
Common Misspellings for LINEAR PROGRAMMING
- kinear programming
- pinear programming
- oinear programming
- lunear programming
- ljnear programming
- lknear programming
- lonear programming
- l9near programming
- l8near programming
- libear programming
- limear programming
- lijear programming
- lihear programming
- linwar programming
- linsar programming
- lindar programming
- linrar programming
- lin4ar programming
- lin3ar programming
Etymology of LINEAR PROGRAMMING
The term "linear programming" was coined by the mathematician George Dantzig in the late 1940s. The word "linear" refers to the fact that the mathematical model used in linear programming consists of linear equations and inequalities. These equations represent the constraints and objectives that must be considered in solving optimization problems. The word "programming" in this context does not refer to computer programming but rather to the original meaning of the term, which is planning or scheduling. Hence, "linear programming" can be understood as the process of planning or scheduling in a linear framework.
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