Chapter 2 Linear Programming Models: Graphical and Computer Methods 2.1 Chapter Questions 1) Consider the following linear programming model: Max X12 + X2 + 3X3 Subject to: X1 + X2 ≤ 3 X1 + X2 ≤ 1 X1‚ X2 ≥ 0 This problem violates which of the following assumptions? A) certainty B) proportionality C) divisibility D) linearity E) integrality Answer: D Page Ref: 22 Topic: Developing a Linear Programming Model Difficulty: Easy 2) Consider the following linear programming model: Min 2X1 +
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Duality in Linear Programming 4 In the preceding chapter on sensitivity analysis‚ we saw that the shadow-price interpretation of the optimal simplex multipliers is a very useful concept. First‚ these shadow prices give us directly the marginal worth of an additional unit of any of the resources. Second‚ when an activity is ‘‘priced out’’ using these shadow prices‚ the opportunity cost of allocating resources to that activity relative to other activities is determined. Duality in linear programming
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RESEARCH PAPER ON LINEAR PROGRAMMING 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 linear programming. Methods and linear programming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company‚
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Linear Programming History of linear programming goes back as far as 1940s. Main motivation for the need of linear programming goes back to the war time when they needed ways to solve many complex planning problems. The simplex method which is used to solve linear programming was developed by George B. Dantzig‚ in 1947. Dantzig‚ was one in who did a lot of work on linear programming‚ he was reconzied by several honours. Dantzig’s discovery was through his personal contribution‚ during WWII when Dantzig
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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
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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
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An Introduction to Linear Programming Steven J. Miller∗ March 31‚ 2007 Mathematics Department Brown University 151 Thayer Street Providence‚ RI 02912 Abstract We describe Linear Programming‚ an important generalization of Linear Algebra. Linear Programming is used to successfully model numerous real world situations‚ ranging from scheduling airline routes to shipping oil from refineries to cities to finding inexpensive diets capable of meeting the minimum daily requirements. In many of these problems
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how I typically set up a problem. First I set up the linear programming model and then develop a parallel set-up to use as input to the Solver add-in. I use this strategy because I first like to set up the problem solution before I worry about setting up the parameters for using Solver. 24. Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators‚ some of whom are perma-nent and some of whom
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TOPIC – LINEAR PROGRAMMING Linear Programming is a mathematical procedure for determining optimal allocation of scarce resources. Requirements of Linear Programming • 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 in linear programming must be expressed in terms of linear equations or inequalities Objective
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Phoenix Computer 1. The incremental salary and training cost associated with hiring a new employee and training him/her to be laptop specialist. * Annual salary for new employee = $27‚000 * Cost for three month training program = $1‚500 per person * New employee undergoes three month training $27‚000/12 = $2‚250 $2‚250*3 months = $6‚750 $6‚750 + $1‚500 =$8‚250 per person The incremental salary and training cost associated with hiring a new employee and training
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