Linear Programming - Meaning, Example and Application in Business
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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.
Linear Programming - Meaning, Example and Application in Business
- 1. Under the guidance of Sundar B. N. Asst. Prof. & Course Co-ordinator GFGCW, PG Studies in Commerce Holenarasipura
- 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