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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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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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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Uniform linear acceleration Introduction This topic is about particles which move in a straight line and accelerate uniformly. Problems can vary enormously‚ so you have to have your wits about you. Problems can be broken down into three main categories: Constant uniform acceleration Time-speed graphs Problems involving two particles Constant uniform acceleration Remember what the following variables represent: t = the time ; a = the acceleration ; u = the initial speed ; v = the final
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the other value and some constant. In other words‚ two variable values (numbers or quantities) are proportional if their ratio is a constant‚ called the coefficient of proportionality or the proportionality constant. This is best explained using the linear equation: y = k*x If k is a constant quantity‚ x will always be proportional to y for every possible value. Then k is considered to be the coefficient of proportionality. Proportion is also the name we use when describing the equality of two
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how they came up with these formulas. For now‚ just memorize them. First‚ notice that the terms in each factorization are the same; then notice that each formula has only one "minus" sign. For the difference of cubes‚ the "minus" sign goes with the linear factor‚ a – b; for the sum of cubes‚ the "minus" sign goes in the quadratic factor‚ a2 – ab + b2. Some people use the mnemonic "SOAP" for the signs; the letters stand for "same" as the sign in the middle of the original expression‚ "opposite" sign
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section I and 35 in section II. Syllabus Section – I (Mental Ability) : Knowing our Numbers‚ Whole Numbers‚ Playing with Numbers‚ Basic Geometrical Ideas‚ Understanding Elementary Shapes‚ Integers‚ Fractions‚ Decimals‚ Data Handling‚ Mensuration‚ Algebra‚ Ratio and Proportion‚ Symmetry‚ Practical Geometry‚ Logical Reasoning. Section – II (Science) : Motion and Measurement of Distances‚ Light‚ Shadows and Reflections‚ Electricity and Circuits‚ Fun with Magnets‚ Air and Water‚ Sorting and Separation
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Accelerated Coordinate Algebra / Analytic Geometry Part A Dr. Khan‚ Ph.D.‚ Fall 2012 ekhan@marietta-city.k12.ga.us WHY ARE YOU TAKING THIS COURSE? All Georgia high school students are required to take four years of mathematics. Taking Accelerated Coordinate Algebra / Analytic Geometry Part A is comparable to taking the typical ninth grade course‚ Coordinate Algebra AND the first half of the tenth grade course‚ Analytic Geometry. The reason for acceleration of the first three courses is to
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involved in economics. Some argue‚ the process is not focused on linear (Sayes 2012; Hughes 2000). An analyses of Ziziphus mauritiana linkage and production process‚ shows that they are a complex web of economic inter-linkages). Contrary to being linear as often suggested. Instead‚ value chains are more space‚ time and socially constructed. The study noted with concern that value chain has been and is still being described as linear (Ash 2013). Suggesting there is a beginning node and the ending
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the polynomial. Classification of polynomials on the basis of degree. 14 ISSUED BY KENDRIYA VIDYALAYA - DOWNLOADED FROM WWW.STUDIESTODAY.COM ISSUED BY KENDRIYA VIDYALAYA - DOWNLOADED FROM WWW.STUDIESTODAY.COM degree Polynomial Example (a) 1 Linear (b) 2 Quadratic etc. (c) 3 Cubic etc. (d) 4 Biquadratic Classification of polynomials on the basis of no. of terms No. of terms Polynomial & Examples. (i) 1 Monomial - (ii) 2 Binomial - (iii) 3 Trinomial- etc. etc. etc. Constant
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