(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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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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spreadsheet modeling and Solver to find the optimal solution of optimization problems. If the model has two variables‚ the graphical method can be used to solve the model. Very few real world problems involve only two variables. For problems with more than two variables‚ we need to use complex techniques and tedious calculations to find the optimal solution. The spreadsheet and solver approach makes solving optimization problems a fairly simple task and it is more useful for students who do not have
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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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QUANTITATIVE METHODS II Mid-Term Examination Monday‚ October22‚ 2012 Time : 150 minutes Total No. of Pages :17 Name ________________________ Total No. of Questions: 3 Roll No. ________________________ Total marks:35 Section: _______________________ Instructions 1. This is a Closed Book Exam. You are not allowed to carry anything other than stationary and calculator. 2. Answer all questions only in the space provided following the question. 3.
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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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DUE: OCTOBER 16‚ 2014 CASE PROBLEM The Southern Textile Mill produces 5 different fabrics. Each fabric can be woven on one or more of the mill’s 38 looms. The sales department’s forecast of demand for the next month is shown in Table 1 along with data on the selling price per yard‚ variable cost per yard‚ and purchase price per yard. The mill operates 24 hours a day and is scheduled for 30 days during the coming month. Fabric Demand Selling Price Variable Cost Purchase Price (yards)
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Chapter 8 Linear Programming Applications To accompany Quantitative Analysis for Management‚ Eleventh Edition‚ Global Edition by Render‚ Stair‚ and Hanna Power Point slides created by Brian Peterson Copyright © 2012 Pearson Education 8-1 Learning Objectives After completing this chapter‚ students will be able to: 1. Model a wide variety of medium to large LP problems. 2. Understand major application areas‚ including marketing‚ production‚ labor scheduling‚ fuel blending‚ transportation‚ and
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Quantitative Methods in Business – Linear Programming 1- Statement of the Problem: Middle East for investment offers a bundle of investment options in many types of securities. Mr. Brown‚ an investor‚ would like to invest $ 5 million in various securities. He wishes to maximize his yearly profit over the next year. The investment company offered him a portfolio including Bonds‚ Stocks‚ Gold and Land. The expected return is 6% for Bonds‚ 14% for Stocks‚ 10% for Gold and 5% for Land. For diversification
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