This document discusses linear programming and its applications. It begins with an introduction and definition of linear programming as a quantitative technique to solve allocation problems. It then provides an example problem formulation to maximize revenue from two products under time and capacity constraints. The document outlines several application areas of linear programming in business, including production management, personnel management, inventory management, marketing management, financial management, and blending problems. It concludes that linear programming is an important mathematical technique for managers to make optimal decisions.

1. Under the guidance of
Sundar B. N.
Asst. Prof. & Course Co-ordinator
GFGCW, PG Studies in Commerce
Holenarasipura

2. Contents:-
Introduction
Meaning
Example
Application areas in
Business
Conclusion
Reference

3. Linear Programming is a powerful quantitative
technique (or operational research technique) designs
to solve allocation problem.
Linear Programming is a special and versatile
technique which can be applied to a variety of
management problems viz, advertising, distribution,
investment, production,refinery operations and
transportation analysis.

4. Linear Programming is a way of solving problems involving two variables
with certain constraints. Usually, linear programming problems will ask us to
find the minimum or maximum of a certain output dependent on the two
variables.
Linear Programming problems are almost always word problems.This
method of solving problems has applications in business, supply-chain
management, hospitality, cooking, forming and crafting among others.
The term linear programming consist of the two words ‘linear’ and
programming. The word ‘linear’ is used to describe the relationship between
decision variables, which are directly proportional.
What is linear programming?

5. Example:-
A company makes two products A and B both require
processing on 2 machines. product A takes 10 and 15 minutes on the
two machines per unit and product B takes 22 and 18 minutes per
unit on the two machines. Both the machines are available for 2640
minutes per week. The products are sold for Rs 200 and Rs 175
respectively per unit. Formulate a Lp to maximize revenue? The
market can take a maximum of 150 units of product A.

6. Formulation:-
1. The market can take a maximum of 150 unisA
2. A) What is objective
B) On which parameters objective is depending
3. To maximize revenue
PROCESSING TIME RIQUIRED (MINUTES) SELLING PRICE
(RS)
MACHINE 1 MACHINE 2
PRODUCT A 10 15 200
PRODUCT B 22 18 175
AVAILABLITY OF
MACHINES
2640 MINUTES PER
WEEK
2640 MINUTES PER
WEEK

7. Subject to the constraints:-
Let X be the number of units of product A so be made
and Y be the number of units of product B so be made
Objective is to maximize Z=200X+175Y
Constraints on time availability of machine-
1=10X+22Y≤2640
Constraints on time availability of machine-
2=15X+18Y≤2640
X≤150 (maximum quantity of product A can be made )
Since the number of units produced for both A and B cannot be
negative, the Non negative restrictions are ; X≥0, Y≥0 (non negative
constraints)

8. Applications of linear programming:-
Applications of linear programming are everywhere
around you. You use linear programming at personal and
professional fronts. Most successful quantitative approach to
decision making, also have been reported almost every industry
application includes.
Business
Marketing
Distribution
Military
Industrial

9. Applications areas in business :-
Blending problem
Financial
management
Marketing
management
Inventory
management
Personnel
management
Production
management

10. 1) Production management:-LP is applied for determining the optimal
allocation of such resources as materials, machines, manpower
etc. by a firm. It is used to determine the optimal product-mix of the
firm to maximize it’s revenue. It is also used for product smoothing
and assembly line balancing.
2) Personnel management:-LP technique enables the personnel manager to
solve problems relating to recruitment, selection, training,and
deployment of manpower to different departments of the firm.It is
also used to determine the minimum number of employees required
in various shifts to meet production schedule within a time
schedule.
3) Inventorymanagement:-A firm is faced with the problem of inventory
management of raw materials and finished products. The objective
function in inventory management is to minimize inventory cost
and the constraints are space and demand for the product. LP
technique is used to solve this problem.

11. 4) Marketing Management:- LP technique enables the marketing manager in
analysing the audience coverage of advertising based on the available media
, given the advertising budget as the constraint.
5) Financial Management:- The financial manager of a firm, mutual fund,
insurance company, bank, etc. uses the LP technique for the selection of
investment portfolio of shares, bonds, etc .so as to maximize return on
investment.
6) Blending problem:-LP technique is also applicable to blending problem when a
final product is produced by mixing a variety of raw materials. The
blending problems arise in animal feed ,diet problems, petroleum products,
chemical products etc.

12. Conclusion:-
Linear programming is very
important mathematical technique which
enables managers to arrive at proper
decisions regarding his area of work. Thus
it is very important part of operations
Research.

13. Reference:-
• https://www.storyofanathematics.com>...
• https://YouTube.be/BFKhrXin30K
• https://YouTube.be/dAhipu3my9c
• https://www.youarticlelibrary.com