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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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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PROBLEM NUMBER 1 A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5‚000 for every acre he plants with wheat and $3‚000 for every acre he plants with barley. His use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires just 1 gallon per acre. What is the maximum profit he can make? SOLUTION TO PROBLEM NUMBER 1 let x = the number of acres of wheat
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from another mill. Fabrics that cannot be woven at the Southern Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table 1. MANAGERIAL REPORT I. - Develop a Linear Programming Model that can be used to schedule production for the Southern Textile Mill‚ and at the same time to determine how many yards of each fabric must be purchased from another mill. The model should be clear and complete.
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(2003) 1 OPERATIONS RESEARCH: 343 1. LINEAR PROGRAMMING 2. INTEGER PROGRAMMING 3. GAMES Books: Ð3Ñ IntroÞ to OR ÐF.Hillier & J. LiebermanÑ; Ð33Ñ OR ÐH. TahaÑ; Ð333Ñ IntroÞ to Mathematical Prog ÐF.Hillier & J. LiebermanÑ; Ð3@Ñ IntroÞ to OR ÐJ.Eckert & M. KupferschmidÑÞ LP (2003) 2 LINEAR PROGRAMMING (LP) LP is an optimal decision making tool in which the objective is a linear function and the constraints on the decision problem are linear equalities and inequalities. It is a very popular
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King Fahd University of Petroleum & Minerals College of Industrial Management Second semester (052) 2005-2006 CASE PROBLEM ( PRODUCT MIX) Prepared for DR Taqi Al-Faraj Group J 225742 Bara’a Al-Jumbaz 4 226352 Mwuaffag Baswaid Ahmad Al-Abdul Muney" 205943 30 May 2006 Case Problem PRODUCT MIX Background: TJ’s Inc.‚ makes 3 nut mixes for sale to grocery chains located in the Southeast. The three mixes are: Regular Mix‚ Deluxe Mix and Holding Mix. They are made by mixing different percentages
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inbound marketing and learn its fundamentals. Read our introductory ebook‚ “An Introduction to Lead Nurturing.” INTERMEDIATE Intermediate content is for marketers who are familiar with the subject but have only basic experience in executing strategies and HubSpot’s All-in-One Marketing Software ... brings your whole marketing world together in one‚ powerful‚ integrated system. Get Found: Help prospects find you online Convert: Nurture your leads and drive conversions Analyze: Measure
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Models Supply Chain Design The Darby Company manufactures and distributes meters used to measure electric power consumption. The company started with a small production plant in EI Paso and gradually built a customer base throughout Texas. A distribution center was established in Fort Worth‚ Texas‚ and later‚ as business expanded‚ a second distribution center was established in Santa Fe‚ New Mexico. The EI Paso plant was expanded when the company began marketing its meters in Arizona‚ California
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Case Study 6 IKEA: Culture as competitive advantage Suggested case discussion questions Q1 Explain how IKEA’s culture contributed to its early expansion efforts IKEA’s culture is encapsulated in the expression the “IKEA-way.” This is the philosophy Ingvar Kamprad formed during the early years of IKEA and drove its expansion efforts. His non-conformist ways gave him freedom to focus and innovate on all facets of distribution. His obsession with low prices‚ led to an unwavering focus
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SMEToolKit.org [pic]Linear programming is very important in various fields of life especially in managerial decision making. The reason is that it helps the company in minimizing the costs and maximizing the profits. Through linear programming managers can calculate the prices and the sales units which can maximize the profits of the company. Therefore‚ there are various issues which the company incurs regarding their costs and prices therefore‚ tools like linear programming can help the managers
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