Linear Programming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of given criterion of optimality.The usefulness of linear programming as a tool for optimal decision-making on resource allocation, is based on its applicability to many diversified decision problems. The effective use and application requires, as on its applicability to many diversified decision problems. The effective use and application requires, as a first step, the mathematical formulation of an LP model, when the problem is presented in words. Steps of linear programming model formulation are summarized as follows : STEP 1 : Identify the Decision Variables

a) Express
each constraint in words. For this you should first see whether the constraint is of the form >/ (at least as large as), of the form \< (no larger than) or of the form = (exactly equal to)

b) You should then verbally express the objective function

c) Steps (a) and (b) should then allow you to verbally identify the decision variables

If there are several decision alternatives available , then in order to identify the decision variables you need to ask yourself the question – what decisions must be made in order to optimize the objective function ?

Having accomplished step 1(a) through (c) decide the symbolic notation for the decision variables and specify units of measurement. Such specification of units of measurement would help in interpreting the final solution of the LP problem .

STEP 2 : Identify the Problem Data

For solving a problem, we need to identify the problem data so as to provide the actual values for the decision variables. For this,...

...RESEARCH PAPER ON
LINEARPROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linearprogramming.
Methods and linearprogramming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company, its distribution on the performers, when placing orders between the performers and the time intervals, to determine the best range of products, in problems of perspective, current and operational planning and management, traffic planning, defining a plan of trade and distribution, in the problems of development and distribution of productive forces, bases and depots of material handling systems, resources, etc. especially widely used methods and linearprogramming model for solvingproblems are savings (choice of resource-saving technologies, preparation of mixes, nesting materials), production, transportation and other tasks.
Beginning of linearprogramming was initiated in 1939 by the Soviet mathematician and economist Kantorovich in his paper...

... LINEARPROGRAMMING
DATE;
5 JUNE, 14
UNIVERSITY OF CENTRAL PUNJAB
INTRODUCTION TO LINEARPROGRAMMINGLinearprogramming (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. Linearprogramming 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.
LinearProgramming 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.
Linearprogramming 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.
LINEARPROGRAMMING; an optimization...

...LINEARPROGRAMMING
INTRODUCTION:
The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programmingproblems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.
The term ‛linear’ means that all inequations or equations used and the function to be maximized or minimized are linear. That is why linearprogramming deals with that class of problems for which all relations among the variables involved are linear.
Formally, linearprogramming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved.
The general form of a linearprogrammingproblem is
Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn
Subject to
a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1
a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2
. . ....

...TOPIC – LINEARPROGRAMMINGLinearProgramming is a mathematical procedure for determining optimal allocation of scarce resources.
Requirements of LinearProgramming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints inlinearprogramming must be expressed in terms of linear equations or
inequalities
Objective Function it maps and translates the input domain (the feasible region) into output range, with
the two-end values called the maximum and minimum values
Restriction Constraints it limits the degree to which we can pursue our objective
Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs
Parameters these are the fixed values in which the model is solved
Basic Assumption of LinearProgramming1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary
1. Proportionality - for example 1:2 is equivalent to 5:10
1. Additivity -...

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[pic]Linearprogramming is very important in various fields of life especially in managerial decision making. The reason is that it helps the company in minimizing the costs and maximizing the profits. Through linearprogramming managers can calculate the prices and the sales units which can maximize the profits of the company. Therefore, there are various issues which the company incurs regarding their costs and prices therefore, tools like linearprogramming can help the managers in decision making progress.
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[pic]Related reading
What Is Role Of Information In Decision Making?
Do you mean any particular kind of information? There are many kinds of information needed...
What Are The Implications For Managerial Decision Making?
It implicates that the decision of the whole thing is made by the manage himself.
Different Ways In Which A Contract Can Be Discharged?
1 Performance 2 the occurrence or failure of a...

...1. Discuss why and how you would use a liner programming model for a project of your choice, either from your own work or as a hypothetical situation. Be sure that you stae your situation first, before you develpp the LP model
Linearprogramming is a modeling technique that is used to help managers make logical and informed decisions. All date and input factors are known with certainty. Linear program models are developed in three different steps:
Formulation
Solution
Interpretation
The formulation step deals with displaying the problem in a mathematical form. Once that is developed the solution stage solves the problem and finds the variable values. During the interpretation stage the sensitivity analysis gives managers the opportunity to answer hypothetical questions regarding the solutions that are generated.
There are four basic assumptions of linearprogramming and they are as follows:
Certainty
Proportionality
Additivity
Divisibility
Linearprogramming is the development of modeling and solution procedures which employ mathematical techniques to optimize the goals and objectives of the decision-maker. Programmingproblems determine the optimal allocation of scarce resources to meet certain objectives....

...975-395-417-4
Optimum Blending of Coal by LinearProgramming for the Power Plant at Seyitömer Coal Mine
K.Erarslan, H.Aykul, H.Akçakoca & N.Çetin
Dumlupınar University, Department of Mining Engineering, 43100, Kütahya, Turkey
ABSTRACT: In this study, a linearprogramming model is developed to determine the optimum coal blend in terms of quality and quantity. Coal with various features is mined from different panels of Seyitömer Lignite Coal District and fed to a nearby power plant. The quality of the coal is extremely variable through the horizontal and vertical directions, which entails the precise planning of coal blending during the mining and stockpiling stages. Otherwise, a large penalty has to be paid to the power plant. In this study, the objective is to match the calorific values required by the power plant. The quality features and production capacities of coal from different panels are determined and are used in quality constraints. The power plant requires coal in two groups, which are of different qualities and quantities. Therefore, two linearprogramming models complementing each other are developed in order to determine the blending conditions that satisfy the needs of the plant. The models are introduced and solved m the LINDO package program. Reasonable solutions are obtained and optimal amounts of blending are handled. The model also allows the evaluation of coal...

...The development of linearprogramming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linearprogramming uses a mathematical model to describe the problem of concern. Linearprogramming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.
LinearProgramming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone using LinearProgramming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linearprogramming. My main argument is that linearprogramming is one of the most optimal ways of resource allocation and making the most money for any company today.
I used (in conjunction with another field supporter – My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linearprogramming users. In addition, I wanted to examine...

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