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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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 across the crime scene
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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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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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SET A: 10897143‚ 10977570‚ 10879587‚ 10870342‚ 10873279‚ 10857133‚ 10661867‚ 10878440‚ 11090782‚ 10770518‚ 10893091 Three electric power plants with capacities of 25‚ 40‚ and 30 million KWh supply electricity to three cities. The maximum demands at the three cities are estimated at 30‚ 35 and 25 million KWh. The price per million KWh at the three cities is given in the table below. [pic] During the month of August‚ there is a 20% increase in demand at each of the three cities‚ which can
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one person gives to or receives from another person‚ information about that person’s needs‚ desires‚ perceptions‚ knowledge‚ or affective states. Communication may be intentional or unintentional‚ may involve conventional or unconventional signals‚ may take linguistic or nonlinguistic forms‚ and may occur through spoken or other modes." In light of the above definition of communication‚ the success of the Linear and Circular model of communication is dependent upon how successful the message is
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This paper is submitted by Anupam Basu LAB (Linear Alkyl Benzene):- For more than 30 years‚ UOP has been a leading innovator in the production of LAB. During that time‚ we’ve developed the state-of-the-art technology you’ll need to ensure that your new or revamped LAB complex operates most efficiently and produces the highest quality product.LAB is the primary raw material used in the production of linear alkyl benzene sulfonate (LAS). LAB is produced from benzene and long chain normal paraffins
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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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Application of linear functions in Economics (or) Application of straight lines in Economics The linear function is one in which ‘y’ is the first degree expression in ‘x’‚ i.e.‚ y = ax + b. The graph of this function is a straight line. The co-efficient of x represents the slope of the line. If a > 0‚ then the lines are upward sloping‚ and if a < 0‚ then the lines are downward sloping Let us explain certain linear equations used in Economics and business. 1. Linear cost curves
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