# Linear Programming

**Topics:**Optimization, Operations research, Linear programming

**Pages:**7 (1396 words)

**Published:**June 10, 2014

QUANTITAVE TECHNIQUES OF BUSINESS

ASSIGNMENT NO;

5

SUBMITTED TO;

PROF. ADNAN

SUBMITTED BY;

NIDA WASIF

ROLL # 54

MC-B

TOPIC;

LINEAR PROGRAMMING

DATE;

5 JUNE, 14

UNIVERSITY OF CENTRAL PUNJAB

INTRODUCTION TO LINEAR PROGRAMMING

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. It is a mathematical technique used in computer modeling to find the best possible solution in allocating limited resources (energy, materials, machines, money etc) to achieve maximum profit or minimum cost. Linear Programming is a method of expressing and optimizing a business problem with a mathematical model. It is one of the most powerful and widespread business optimization tools. Linear programming can be used in very large variety of business problems. They include: transportation distribution problems

production scheduling in oil & gas, manufacturing, chemical, etc industries financial and tax planning

human resource planning

facility planning

fleet scheduling.

LINEAR PROGRAMMING; an optimization technique capable of solving an amazingly large variety of business problems. A business objective, business restrictions, and costs/revenue are formulated into a mathematical model. Algorithms for finding the best solutions are used. The concept behind a linear programming problem is simple. It consists for four basic components: Decision variables represent quantities to be determined

Objective function represents how the decision variables affect the cost or value to be optimized (minimized or maximized) Constraints represent how the decision variables use resources, which are available in limited quantities Data quantifies the relationships represented in the objective function and the constraints.

EXAMPLE LINEAR PROGRAMMING USES

Production planning in a chemical plant. This model optimized the operation of each unit and the use of storage facilities to meet demand at least cost. Refinery scheduling. Similar to the above but more than one location was involved and distribution to the customers was included. Tax model. Personal and corporate taxes can be minimized using a linear programming model. It includes the best mix of dividends and salaries and the progressive personal tax rates. Truck designs. The axle spacing on trucks are subject to complex loading rules. In some provinces, the design of these axle spacing can be modeled using linear programming to maximize load. DEVELOPING LINEAR PROGRAMMING MODEL

Model: A structure which has been built purposefully to exhibit features and characteristics of some other object such as “DNA model” in biology, a “building model” in engineering etc. Steps in formulating Linear Programming Model:

Following are the steps involved in formulating a linear programming model: Step 1:

It is always good to place all information in a tabular format. It is always easy and good to understand. Step 2:

List all the constraints. Constraints are the restrictions that are always present in every model. Step 3:

Decide what the decision variables are going to be. Step 4:

Determine the objective function. In this the objective is determined that is to maximize the profits or minimize the costs. Step 5:

Develop equations for the numerical valued...

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