Define Linear Programming.

Linear Programming (LP) is a mathematical method used to optimize the allocation of limited resources among competing activities or demands, subject to linear constraints. The goal of linear programming is to maximize or minimize a linear objective function, representing a measurable quantity such as profit, cost, time, or resource utilization.

In LP, decision variables are defined to represent quantities to be determined, and these variables are subject to linear constraints that represent limitations or requirements on these variables. Constraints can include restrictions on available resources, capacity limits, and operational requirements.

The basic components of a linear programming problem include:

1. Objective Function: A linear equation representing the quantity to be maximized (e.g., profit) or minimized (e.g., cost).
2. Decision Variables: Variables representing quantities to be determined or optimized.
3. Constraints: Linear inequalities or equations that impose limitations or requirements on the decision variables based on available resources, capacities, or operational constraints.

LP problems are typically solved using optimization techniques to find the values of decision variables that optimize (maximize or minimize) the objective function while satisfying all constraints. Common methods for solving LP problems include the simplex method, graphical method, and software-based algorithms like interior point methods. Linear programming finds applications in various fields including operations research, economics, engineering, finance, and supply chain management.