Topics on "Operational Research" Mar. 2007‚ IST Linear Programming‚ an introduction MIGUEL A. S. CASQUILHO IST‚ Universidade Técnica de Lisboa‚ Ave. Rovisco Pais‚ IST; 1049-001 Lisboa‚ Portugal Linear Programming is presented at an introductory level‚ mainly from the book by Hillier and Lieberman [2005]‚ abridged and adapted to suit the objectives of the “Operational Research” course. It begins with segments of its third chapter. Key words: linear programming; simplex method. I. Fundamentals
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Solving systems of linear equations 7.1 Introduction Let a system of linear equations of the following form: a11 x1 a21 x1 a12 x2 a22 x2 ai1x1 ai 2 x2 am1 x1 am2 x2 a1n xn a2 n x n ain xn amn xn b1 b2 bi bm (7.1) be considered‚ where x1 ‚ x2 ‚ ... ‚ xn are the unknowns‚ elements aik (i = 1‚ 2‚ ...‚ m; k = 1‚ 2‚ ...‚ n) are the coefficients‚ bi (i = 1‚ 2‚ ...‚ m) are the free terms
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It seems that the Renaissance (1300-1700)‚ methods of presenting the surrounding world in a flat pictorial plane using linear perspective‚ has dictated the way artists have worked for countless centuries. Linear perspective is a technique used by artists that uses line to create the illusion of depth and space within their work. However this approach is only a representation created using a singular eye. This method of working is suggested to have originated from Leon Battista Alberti’s (1404-1472)
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Search patterns vary and depend on the type of scene‚ the victims and suspect’s actions as well as the location and size of the area. Having someone in command can eliminate or lessen the chances of evidence or effort being duplicated. While each scene and victim may need a different search pattern‚ each pattern searches the probable points of entry first and any exits possibly used by the criminal. A line/strip search is one that is used by one or two investigators who walk in straight lines
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1. Problem Statement Keisha is making a quilt that will be made up of rectangular patches of rectangular material. When she finds a box of satin material that is 17 by 22 inches long she wonders how many 3 by 5 inch patches she could include into the quilt. However‚ after we found out that 22 at minimum‚ rectangular patches can fit into the quilt and 24 at maximum‚ she decides to see how many 9 by 10‚ 10 by 12 and 8 by 9 inch boxes she can fit into the 17 by 22 inch quilt. Lastly‚ she had to
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A Digital Proof Write-up The problem in A Digital Proof has two parts. The first is to fill in five boxes with numbers that fit the criteria: each box has a number‚ and the digit that is placed in each box must be the amount of times that number appears in the whole five digit number formed by the boxes. The second part of the problem is to prove that there is only one solution. How I went about solving this problem was somewhat simple; at least‚ it was at first. I started from the ‘four’ box
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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
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POW 11: Let’s Make A Deal 1. Problem Statement: For this Problem of the Week we were required to find out if our chances of winning Let’s Make A Deal were higher if we switched to the other door or stayed with our original door after a worthless prize was revealed behind one of the doors we did not chose. The game show host knew what was behind each door‚ so every time he would reveal something worthless behind one of the doors you did not choose after you made your first choice. Then he would
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Linear Programming Concept Paper There are two types of linear programming: 1. Linear Programming- involves no more than 2 variables‚ linear programming 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. Linear programming is a useful technique to solve such problems. The necessary condition is that the data must be
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Proceedings of the 2010 International Conference on Industrial Engineering and Operations Management Dhaka‚ Bangladesh‚ January 9 – 10‚ 2010 Application of Integer Linear Programming Model for Vendor Selection in a Two Stage Supply Chain A. John Rajan Department of Mechanical and Production Engineering Sathyabama University‚ Chennai‚ India K. Ganesh Senior consultant‚ Global Business Services‚ IBM India Private Limited‚ Mumbai‚ India K.V. Narayanan Controller of Examinations‚ Sathyabama
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