Chapter 2 Linear Programming: Basic Concepts Solution to Solved Problems 2.S1 Back Savers Production Problem Back Savers is a company that produces backpacks primarily for students. They are considering offering some combination of two different models—the Collegiate and the Mini. Both are made out of the same rip-resistant nylon fabric. Back Savers has a long-term contract with a supplier of the nylon and receives a 5000 square-foot shipment of the material each week. Each Collegiate requires
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17th International Mining Congress and Exhibition of Turkey- IMCET 2001‚ © 2001‚ ISBN 975-395-417-4 Optimum Blending of Coal by Linear Programming 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 linear programming model is developed to determine the optimum coal blend in terms of quality and quantity. Coal with various features is mined from different
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PERSONAL FINANCIAL INVESTMENT STRATEGY ANALYSIS [pic] PROBLEM: Bob and Pina Ing‚ 31 and 28‚ a newly-wed couple found themselves in the midst of an interesting decision making problem. It appeared that their fortune had turned overnight when they won a mega lottery and received one million dollars after tax in price money. They were confused about how to invest their money‚ such that it gives them the maximum return on their investment. The couple consulted Jayhawks Financial Services LLC
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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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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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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‚ the number
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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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CheckPoint: Programming Problems Complete the programming problems 1 and 2 as described below. DO NOT COMPLETE THE PROBLEMS FROM THE TEXT For each of the following problems‚ use the top-down modular approach when writing the pseudocode to design a suitable program to solve each problem. Be sure to include an “analysis” for each problem. Note: you need to write 2 separate programs that will handle each problem separately. That means you will also have 2 analyses. Problem 1 Design a program
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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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Z00_REND1011_11_SE_MOD7 PP2.QXD 2/21/11 12:39 PM Page 1 7 MODULE Linear Programming: The Simplex Method LEARNING OBJECTIVES After completing this chapter‚ students will be able to: 1. Convert LP constraints to equalities with slack‚ surplus‚ and artificial variables. 2. Set up and solve LP problems with simplex tableaus. 3. Interpret the meaning of every number in a simplex tableau. 4. Recognize special cases such as infeasibility‚ unboundedness and degeneracy. 5
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