George Dantzig and his associates developed linear programming in 1947 to solve military planning problems for the US Air Force. Linear programming models represent organizational activities as a linear objective function to determine the optimal allocation of scarce resources like materials, money, and time among competing demands. It uses a simplex method to solve the linear programming problem. Linear programming consists of linear objectives and constraints where variables have a proportionate relationship, like increased labor increasing production. The goal is to maximize or minimize the objective function subject to the constraints.

1. (LP)

2. Linear Programming
Generalized Linear Programming Models
Solutions to LP Models by Graphical Methods
Solutions to LP Models by Simplex Methods
Big M Method
Duality in LP Models

3. Introduction of LP Models
It was in 1947 that George Dantzig and his
associates found out a technique for solving
military planning problems while they were
working on a project for US Air Force.
Afterwards, Dantzig suggested this approach
for solving business and industrial problems.

4. This technique consisted of representing the
various activities of an organization as a Linear
Programming model and arriving at the optimal
program by minimizing/ maximizing a linear
objective function.
Dantzig also developed the most powerful
mathematical tool known as “Simplex Method”
to solve linear programming problem.

5. Linear Programming is a
widely used
mathematical modeling
technique to determine
the optimum allocation
of scarce resources
among competing
demands.
Resources typically
include raw materials,
manpower, machinery,
money, time and space
etc.

6.  As its name implies,
the linear programming model consists of
linear objectives and linear constraints,
which means that
the variables in a model have a
proportionate relationship.
 For example, an increase in labour resource
(input) will result an increase in production
(output).

7. FORMULATION
• Maximization
• Minimization
Objective
Function
• ≤ (Max. Availability)
• ≥ (Min. Requirement)
• = (Standard)
Constraints
(Conditions)
• (always)
• ≥ 0
Non
Negativity