Linear Programming (LP), also known as Linear Optimization, is a mathematical method used to determine the best possible outcome—such as maximum profit or minimum cost—given a set of linear constraints. These constraints can be in the form of equations or inequalities, and the goal is to optimize a linear objective function.

LP is widely used in business, economics, engineering, and logistics to solve problems involving limited resources. The method focuses on identifying the feasible region defined by the constraints and finding the point within this region that optimizes the objective.

Key Assumptions of Linear Programming:

  • Constraints must be measurable and expressed in quantitative terms.

  • The relationships among variables and constraints must be linear.

  • The objective function to be optimized (maximized or minimized) must also be linear.

In essence, linear programming helps in making the best decision under given conditions by modeling real-world problems with mathematical precision.

Components of Linear Programming

Linear Programming problems consist of four key components:


  1. Decision Variables: 
      • The unknowns you need to determine (e.g., how many products to make).
  2. Constraints: 
      • The limitations or rules (e.g., budget, time, resources) expressed as linear inequalities or equations.
  1. Data: 
      • The numerical values (like costs or resource limits) used in the model.
  1. Objective Function: 
      • A linear function to maximize or minimize (e.g., profit or cost).