# Linear Programming .

December 26, 2020**Linear programming** (**LP**, also called **linear optimization**) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

## History :

Leonid KantorovichJohn von Neumann

The problem of solving a system of linear inequalities dates back at least as far as Fourier, who in 1827 published a method for solving them, and after whom the method of Fourier–Motzkin elimination is named.

In 1939 a linear programming formulation of a problem that is equivalent to the general linear programming problem was given by the Soviet mathematician and economist Leonid Kantorovich, who also proposed a method for solving it. It is a way he developed, during World War II, to plan expenditures and returns in order to reduce costs of the army and to increase losses imposed on the enemy. Kantorovich’s work was initially neglected in the USSR.

**What is linear programming used for **:

**Linear programming** is **used for** obtaining the most optimal solution for a problem with given constraints. In **linear programming**, we formulate our real-life problem into a mathematical model. It involves an objective function, **linear** inequalities with subject to constraints.Feb 28, 2017.

**What are the three components of a linear program** :

Constrained optimization models have three major components: decision variables, **objective function**, and constraints.

**How is LPP calculated** :

**Answer: In order to calculate LPP, one must follow the following steps:**

- Formulate the LP problem.
- Construct a graph and then plot the various constraint lines.
- Ascertain the valid side of all constraint lines.
- Identify the region of feasible solution.
- Plot the objective function.
- Finally, find out the optimum point.