The development of linear programming 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. Linear programming uses a mathematical model to describe the problem of concern. Linear programming 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. Linear Programming 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 Linear Programming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linear programming. My main argument is that linear programming 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 linear programming users. In addition, I wanted to examine the effect of the use of linear programming across three different but key decision support areas of the participating companies to include (1) Planning (2) Forecasting and (3) Resource Allocation. The companies were selected randomly from the Dunn & Bradstreet Database of companies and also from the CNN and Yahoo Databases of company performances. All these data sources are available free of charge. The three key measures that I wanted to use to examine the impact of LP on company results were EPS, (Earnings per Share; explained later) the ROI%, (Rate on Investment or the Rate of Return; explained later) and Profit. I used these three measures as they are key measures that Wall Street Investors look at when they examine 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 +...

... 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...

...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...

... 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...

...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...

...sal11586_ch08.qxd
10/10/03
10:12 AM
Page 336
Chapter
8
LinearProgramming
CHAPTER OUTLINE
KEY TERMS
Linearprogramming
Production process
Feasible region
Optimal solution
Objective function
Inequality constraints
Nonnegativity constraints
Decision variables
Binding constraints
Slack variable
Simplex method
Primal problem
Dual problem
Shadow price
Duality theorem
Logistic management
8-1 Meaning, Assumptions, and Applications ofLinearProgramming •
The Meaning and Assumptions of LinearProgramming • Applications
of LinearProgramming
8-2 Some Basic LinearProgramming Concepts • Production Processes
and Isoquants in LinearProgramming • The Optimal Mix of Production
Processes
8-3 Procedure Used in Formulating and Solving LinearProgramming
Problems
8-4 LinearProgramming: Profit Maximization • Formulation of the
Profit Maximization LinearProgramming Problem • Graphic Solution of
the Profit Maximization Problem • Extreme Points and the Simplex
Method • Algebraic Solution of the Profit Maximization Problem •
Case Study 8-1: Maximizing Profits in Blending Aviation Gasoline and
Military Logistics by LinearProgramming • Case Study 8-2: Linear...