LINEAR ALGEBRA Paul Dawkins Linear Algebra Table of Contents Preface............................................................................................................................................. ii Outline............................................................................................................................................ iii Systems of Equations and Matrices.............................................................................................
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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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Department of MECH an ica l.in Paavai Institutions ch UNIT II ww w. me LINEAR AND ANGULAR MEASUREMENTS UNIT-II 2. 1 Department of MECH CONTENTS LINEAR MEASURING INSTRUMENTS 2.1.1 SCALES 2.1.2 CALIPERS 2.1.3 VERNIER CALIPERS 2.1.4 MICROMETERS 2.1.5 SLIP GAUGES 2.3 LIMIT GAUGES 2.4 PLUG GAUGES 2.5 TAPER PLUG GAUGE 2.6 RING GAUGES 2.7 SNAP GAUGE 2.8 TAYLOR’ S PRINCIPLE 2.9 COMPARATORS
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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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Problem statement. There’s this game called linear nim where 2 players who have 10 marks and so they have to figure out a strategy. Then who ever crosses out the last mark wins. You can also play it with 15 marks. But you have to figure what to do while playing this game and try to find patterns or strategies to win. Process. So what I did to attempt the problem is that I played the game a few times with my partner with the 10 marks and 15. So we can find some patterns and strategies that we can
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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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A. DETERMINE IF BLOOD FLOW CAN PREDICT ARTIRIAL OXYGEN. 1. Always start with scatter plot to see if the data is linear (i.e. if the relationship between y and x is linear). Next perform residual analysis and test for violation of assumptions. (Let y = arterial oxygen and x = blood flow). twoway (scatter y x) (lfit y x) regress y x rvpplot x 2. Since regression diagnostics failed‚ we transform our data. Ratio transformation was used to generate the dependent variable and reciprocal transformation
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Linear Programming Tools and Approximation Algorithms for Combinatorial Optimization by David Alexander Griffith Pritchard A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Combinatorics and Optimization Waterloo‚ Ontario‚ Canada‚ 2009 c David Alexander Griffith Pritchard 2009 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis‚ including any required final revisions
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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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the diet plan: The chicken food type should contribute at most 25% of the total calories intake that will result from the diet plan. The vegetable food type should provide at least 30% of the minimum daily requirements for vitamins. Provide a linear programming formulation for the above case. (No need to solve the problem.) Element | Milk | Chicken | Bread | Vegetables | Calories (X1) | 160 | 25% * 210 | 120 | 150 | Carbohydrates (X2) | 110 | 130 | 110 | 120 | Protein (X3) | 90 | 190
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