Linear programming is a technique which shows practical problems as a series of mathematical equations which can be manipulated to find the optimum or best solution. Blending is a graphical approach to linear programming which deals with resource allocation subject to constraints. It is a model which assists firms in deciding the best possible utilisation of limited resources. Each resource constraint is represented as a mathematical linear equation. A linear expression is an equation which links two variables, and if plotted on a graph, would be represented by a straight line. By plotting all the equations, the optimal use of the business's resources can be easily identified.

Blending can be useful to firms when deciding how to make the best use of their resources. Businesses can use this method to allocate factors of production so that profits are maximised or costs minimised, depending on the business's objective. Another advantage of blending is that is allows the business to decide a combination of the two goods to produce, as compared to other invest appraisal or decision making techniques where either one or the other option must be selected, but not both.

Blending is a fairly easy and fast technique as it only requires simple calculations. The results are also represented on a graph and so information can be seen visually and do not require much explanation. Additionally, computers can speed up the calculations and increase the methods accuracy.

However, blending has its limitations. It does not take into account the market demand for the products. The assumption is that the optimum output level for each good will be sold profitably, which may not be the case. Producing at the most profitable output level will not matter if the products cannot be sold.

This technique also assumes that resources can be switched between the two products at a constant rate of productivity. This may not be a realistic assumption. For example, the machines in a...

...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. Programming problems 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 linearprogramming problem is
Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn
Subject to
a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1
a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2
. . . .
am1 x1+ am2 x2 +...

...ISBN 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...

... 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 technique capable of solving an amazingly...

...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 solving problems 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 "Mathematical methods of organizing and planning production." The appearance of...

... Homework for linear and integer programming
(due: final exam )
Note: 1) All problems should be solved by Lingo
2) Attach Lingo formulation and Output.
Problem 1 (5 pts)
The Friendly family grows apples on its farm, which they harvest each fall and make into 3 products, apple butter, apple sauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm pumpkin Festival for two weeks in October. Their 3 primary resources are cooking time in their kitchen, their own labor time, and the apples. They have a total of 500 cooking hours available, and it requires 3.5 hours to cook a batch of butter, 5.2 hours to cook a batch of sauce, and 2.8 hours to cook a batch of jelly. A batch of butter requires 1.2 hours of labor, a batch of sauce take 0.8 hours, and a batch of jelly requires 1.5 hours. They have 240 hours of labor available during the fall. They produce about 6500 apples each fall. Leftover apples can be discarded at no cost. A batch of butter requires 40 apples, a batch of sauce requires 55 apples, and a batch of jelly requires 20 apples. After the products are canned, sales revenue will equal $190, $170, and $155 per batch of butter, sauce, and jelly, respectively. The family wants to know how many batches of each type of product to make in order to maximize their sales revenue
Formulate a linear...

...LinearProgramming Concept Paper
There are two types of linearprogramming:
1. LinearProgramming- involves no more than 2 variables, linearprogramming problems can be structured to minimize costs as well as maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. Linearprogramming is a useful technique to solve such problems.
The necessary condition is that the data must be expressed in quantitative terms in the form of linear equations and inequalities. The general nature of the business problems in which linearprogramming can be effectively used are multifaceted. They include purchasing, transportation, job assignments, production scheduling and mixing. Linearprogramming provides a method of maximizing or minimizing a first degree function subject to certain environmental restrictions or constraints which are usually in the form of equations and inequalities.
2. Simplex method- is an algorithm for solving linearprogramming with any number of variables. Most real-world linearprogramming problems have more than two variables and thus are too complex for graphical solution. A...

...Karen Boyd,
Matt Beaumont.
Executive Summary:
Filatoi Riuniti is expanding to meet growing demand, and we have used outsourcing to keep up. Currently, we outsource only coarse and medium-sized yarn, but we believe that it would be more efficient to look at outsourcing all types. There are so many potential suppliers and constraints to consider that we constructed a linearprogramming model to identify our best option and check our solution's sensitivity to changes in our situation.
We've analyzed our potential suppliers for each gauge, taking into account their capacity, cost of production for each plant, and transportation costs (The model and our objective function can be found in the appendix.) Our goal was to allocate spinning production (at Filatoi Riuniti and six local mills) in a manner that would minimize overall costs, while meeting the demand and operating within the capacity constraint of each plant. Given the output of our optimization model, we should be outsourcing the spinning of our yarn in this way:
Sensitivity Analysis for Linear Optimization model:
Keep in mind that this model is sensitive to changes in each constraint, and there are ways that we can reduce our costs in the long run. We took into account several specific changes that management identified as probable and sought to see how they would change our optimal production strategy.
First, we wanted to...

...INVESTMENT STRATEGY REPORT
Submitted to J. D. Williams, Inc.
By
Mizar Gonzalez
Industrial Engineering Department
Southern Polytechnic State university
404-519-2792
February 20, 2008
EXECUTIVE SUMMARY
This report is our recommendation for an optimal investment strategy that would allow J. D. Williams, Inc. to maximize the annual yield of an investment of $800,000 in a diversified portfolio of funds.
To find the investment that would result in the greatest annual yield we have formulated a linear program that takes into account the requirements for the client of J. D. Williams, Inc. The requirements for the investment portfolio can be found on the section titled “Problem Description”
The greatest annual yield that can be expected while subject to the requirements of the different funds and the prospective client is $94,133.33. The money has to be invested in the following manner to achieve this result: The amount to be invested in the growth fund must be $ 248,889. The income fund must have an investment of $ 160,000 and the money market fund must have an investment of $ 391, 112.
PROBLEM DESCRIPTION
J. D. Williams, Inc. has a client who wishes to invest $800,000 with the firm in order to maximize his yield after a period of one year. The firm wants to allocate the funds while accommodating some requirements related to portfolio composition and the risk index of the funds as well as the client.
The portfolio must have...