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Words 1271

Pages 6

Input-Output Analysis

Introduction:

There are several non-mathematical subjects that linear algebra can be applicable too. Economics is a topic that linear algebra can be used to make a formal application, for example in Input-Output Analysis, econometrics, Game theory, and break-even point analysis. As a group we are going to be focusing on the Input-Output analysis, a type of analysis created for the purpose of describing and making predictions of complicated mathematical models using systems of linear equations. It was established by “W. Leontief, who won the 1973 Nobel Prize in Economics” (Hefferon, p.60). In this paper, mathematical and linear algebra formulas, calculations, graphs, diagrams, pictures, etc., will be clearly shown as to further understand the applicability of linear algebra in economics. Calculations and mathematical examples used in economics will be provided in the context of this paper for better understanding. Also, terms and notations used will be explained, derivation and origin of mathematical results will be shown.

Definitions:

Economics is a branch of knowledge concerned with the production, distributions, and consumption of goods and services.

Linear algebra is a branch of mathematics with the properties of finite dimensional vector spaces and linear mapping between the spaces. The equations are represented using matrices and vectors and consist of several unknowns.

Econometrics is branch of economics that aims to give the definitions of application of mathematics and statistical methods to economic data.

Game theory is a method of studying strategic decision-making, that is, the study of mathematical models of conflict and cooperation between decision makers (Levine).

Input-output Analysis Application:

The economy is a complicated network of sectors that interact with each…...

...Subject: Global & Applied Economics Subject code: ECO 2263 Lecturer: Ms Sandra Submission date: 29th October 2012 STUDENT PARTICULARS Name: Xu Tieyang Student ID no: SCM-016679 Course: Bachelor of Business Management (Hons) Password: G54049654 Table of Content 1.0 Introduction on social media -------------------------------------------------------------3 2.1 Explain the meaning of social media---------------------------------------------3 2.2 Provide example of social media------------------------------------------------3 2.3 Explain the usage of social media in global businesses---------------------5 2.0 The advantages and opportunities created by social media------------------------5 3.0 disadvantages of social media----------------------------------------------------------7 4.0 Conclusion--------------------------------------------------------------------------------9 5.0 Reference-------------------------------------------------------------------------------10-11 1.0 Introduction on social media 1.1 Explain the meaning of social media These are so many examples for social media, such as Twitter, Facebook, and Pinterest. Here, that’s sure you heard all these words, you should add it in the lowest on other three website list, and then start from scratch to find. But you know what social media is?? Social media is a kind of online media type, can speed up the steps of the traditional media's......

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...Week Four Assignment: Ch.8 & Ch.9 Keidra Conner BUS 640 Managerial Economics October 15, 2012 Ch.8 Applied Problem 2 2. At a management luncheon, two managers were overheard arguing about the following statement: “A manager should never hire another worker if the new person causes diminishing returns.” Is this statement correct? If so why? If not, explain why not. Yes, this statement is correct because in some cases hiring new workers can become negative and cause the marginal product to fall. The text states the managers beyond the point of diminishing returns but not to the point of negative marginal product (Thomas & Maurice, 2011, pp. 296-297). Ch.9 Applied Problems 2 & 4 2. The largo Publishing House uses 400 printers and 200 printing presses to produce books. A printer’s wage rate is $20, and the price of a printing press is $5,000. The last printer added 20 books to total output, while the last press added 1,000 books to total output. Is the publishing house making the optimal input choice? Why or Why not? If not, how should the manager of Largo Publishing House adjust input usage? No, the publishing house is not making the optimal input choice because this is not the least-cost combination of inputs. The manager should hire another printer to maximize the output at a lesser cost. This will balance the amount of inputs for maximizing production of the given output. 4. The MorTex Company assembles garments entirely by hand even though a......

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...valuation; Mergers and acquisitions 2. Accounting for Financial Statements: Preparation of income statement, balance sheet and statement of cash flows: Accounting for specialized items: Property, Plant & Equipment, bad debts; provisions; financial instruments; leases; employee benefits; income taxes; revenues,; foreign currency transactions etc.;Accounting for mergers and consolidations; IFRS vs GAAP; Financial statement analysis 3. Cost and Management Accounting: Cost concepts; Job-order costing vs process costing;ABC Costing; Marginal costing vs absorption costing: CVP analysis; Relevant costs: special order, make or buy decisions; ROA, residual income and economic value added; Standard costing and variance analysis; EOQ and linear programming 4. Quantitative Methods and Business Mathematics: Algebra and logarithm; Series and progressions; Probability, confidence intervals and testing; Measures of central tendency and measures of dispersion; Simple and compound interest: compounding and discounting;Differentiation and integration; Regression and correlation 5. Business Management: Vision, mission and strategy; Human resource management : recruitment and retention, performance measurement and development, compensation, employee rations and ethics etc.; Marketing; Organizational culture, organizational change and effective communication; Business analyses: SWOT, PESTLE, balanced scorecard 6. Microsoft Excel 2003/2007/2010: Financial......

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...more I want to continue to turn the pages and see what else he is going to speak about. Capra starts off Chapter 7 speaking of a subject matter that I have had interest in for quite some time…economics. Capra mentions that the ‘Cartesian framework is often quite inappropriate for the phenomena they are describing, and consequently their models have become increasingly unrealistic’ (1982, 188). Capra specifically mentions that this thought is quite prevalent in economics. I yearn to understand exactly where he is going with this thought, so I read on. I have always believed that the social sciences needed to blend their ideas and theories with economists and political scientists, sociology, and historians, as their basic forces are related to one another. From Academia to our government, this fragmentary approach needs to change as all need to combine all forces from each field to develop wider viewpoints. For instance, ‘Economists generally fail to recognize that the economy is generally one aspect of the whole ecological and social fabric; a living system composed of human beings in continual interaction with one another and with their natural resources, most of which are, in turn, living organisms’ (Capra 1982, 188). Isn’t that an amazing statement? I have always viewed economics in that way, but I could never come up with such a bold way to state the obvious! Economies by nature are continuously changing as they expand and contract. ‘To understand it we need......

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...Applied Economic Theory United States Mortgage Crisis After rising at an annual rate of nearly 9 percent from 2000 through 2005, house prices have decelerated, even falling in some markets. At the same time, interest rates on both fixed- and adjustable-rate mortgage loans moved upward, reaching multi-year highs in mid-2006. Some subprime borrowers with ARMs, who may have counted on refinancing before their payments rose, may not have had enough home equity to qualify for a new loan given the sluggishness in house prices. In addition, some owners with little equity may have walked away from their properties, especially owner-investors who do not occupy the home and thus have little attachment to it beyond purely financial considerations. Regional economic problems have played a role as well; for example, some of the states with the highest delinquency and foreclosure rates are among those most hard-hit by job cuts in the auto industry. The rate of serious delinquencies--corresponding to mortgages in foreclosure or with payments ninety days or more overdue--rose sharply during 2006 and recently stood at about 11 percent, about double the recent low seen in mid-2005.3 The rate of serious delinquencies has also risen somewhat among some types of near-prime mortgages, although the rate in that category remains much lower than the rate in the subprime market. The rise in delinquencies has begun to show through to foreclosures. In the fourth quarter of 2006, about 310,000...

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...sign. Factor - if a is a factor of b, then b is divisible by a. Factorial - operation that multiplies a whole number by every counting number smaller than it. Formula - rule or method that is accepted as true and used over and over in common applications. Fraction - ratio of two numbers representing some portion of an integer. Fundamental theorem of algebra - guarantees that a polynomial of degree n, if set equal to 0, will have exactly n roots. Function - a relation whose inputs each have a single, corresponding output. Graph - plotted figure in a plane. Greatest common factor - the largest factor of two or more numbers or terms. Grouping symbols - elements like parentheses and brackets that explicitly tell you what to simplify first in a problem. Horizontal line test - tests the graph of a function to determine whether or not its one to one. Hypotenuse - longest side of right triangle. i - The imaginary value square root of -1. Identity element - the number(0 for addition, 1 for multiplication) that leaves a numbers value unchanged when the corresponding operation is applied. Imaginary number - has form bi, where b is a real number and i = the square root of -1. Improper fraction - a fraction whose numerator is greater than its denominator. Inconsistent - describes a system of equations that has no solution. Indirect Variation - exhibited by two quantities, x and y, when their product remains constant even as the values of......

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... 1 0 0 1 0 1 0 2 0 0 1 -1 Yes there is a Linear combination: p= q1+2q2-q3 2. A=[1 -2 3 1; 3 0 -2 0; 1 1 -2 0]; rref(A) 1.0000 0 0 0.6667 0 1.0000 0 1.3333 0 0 1.0000 1.0000 Yes there is a Linear Combination: p= 0.67q1 + 1.333q2 + q3 3b 1. A=[1 2 0 2; 2 0 4 1; 0 3 -3 1; 1 -1 3 1]; rref(A) 1 0 2 0 0 1 -1 0 0 0 0 1 0 0 0 0 The given p row is not a linear combination of the q vectors as they do not span all elements in p. 2. A=[1 2 0 1; 2 0 4 18; 0 3 -3 -12; 1 -1 3 13]; rref(A) 1 0 2 9 0 1 -1 -4 0 0 0 0 0 0 0 0 The given p row is a linear combination of the q vectors as they = span all elements in p 3c 1. A=[2 1 1 1; 1 -1 2 0; -3 0 0 0; 4 1 0 0]; rref(A) 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 P is not linear combination of Q 2. A=[2 1 1 0; 1 -1 2 1; -3 0 0 0; 4 1 0 0]; rref(A) 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 P is not linear combination of Q...

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...MATH 4450 - HOME WORK 5 (1) Let V be a R−vector space and < , > be an inner product. Prove that if {v1 , · · · , vn } is a set of mutually orthogonal non-zero vectors, then this set is also linearly independent. Proof: We are given (vi , vj ) = 0 if i = j and (vi , vi ) = 1. To prove that the set if linearly independent, we set a1 v1 + · · · + an vn = 0. Now taking inner product with vj on both sides, we get n ai (vi , vj ) = (0, vj ). Since inner products are linear in the ﬁrst i=1 variable, we get n ai (v1 , vj ) = 0, and this gives aj = 0. Thus we are done. i=1 (2) Let V be a vector space and < , > be an inner product. Then show that (a) < 0, v >= 0 for any v ∈ V . Proof: < 0, v >=< 0 + 0, v >=< 0, v > + < 0, v >. Subtracting < 0, v > from both sides, we get < 0, v >= 0. (b) Show that for a ﬁxed u ∈ V , < u, v >= 0 for any v ∈ V , then u = 0. Proof: Take v = u. Then we have < u, u >= 0, i.e., ||u||2 = 0. This implies that u = 0. (3) Let V be a vector space and < , > be an inner product and B = {v1 , · · · , vn } be an orthonormal basis for V . If c1 , · · · , cn ∈ K are scalars, then show that there is a unique v ∈ V such that < v, vi >= ci . Proof: Let v = n ci vi . Now taking inner product with vj on both sides, we get i=1 (v, vj ) = n ci (vi , vj ). Orthogonality implies that (vi , vj ) = 0 for i = j. Hence we get i=1 (v, vj ) = cj (vj , vj ). Since vj is non-zero (why?), we get ci = (v, vj )/||vj ||2 = (v, vj ). This proves existence. Uniqueness follows from the......

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...SCHAUM’S outlines SCHAUM’S outlines Linear Algebra Fourth Edition Seymour Lipschutz, Ph.D. Temple University Marc Lars Lipson, Ph.D. University of Virginia Schaum’s Outline Series New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2009, 2001, 1991, 1968 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-154353-8 MHID: 0-07-154353-8 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-154352-1, MHID: 0-07-154352-X. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative please e-mail us at bulksales@mcgraw-hill.com. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies...

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...Linear programming of basic economic parameters used at reengineering in small and medium enterprises 1. INTERNATIONAL JOURNAL OF MANAGEMENT (IJM) International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 – 6510(Online), Volume 4, Issue 2, March- April (2013)ISSN 0976-6502 (Print)ISSN 0976-6510 (Online)Volume 4, Issue 2, March- April (2013), pp. 31-43 IJM© IAEME: www.iaeme.com/ijm.asp ©IAEMEJournal Impact Factor (2013): 6.9071 (Calculated by GISI)www.jifactor.com LINEAR PROGRAMMING OF BASIC ECONOMIC PARAMETERS USED AT REENGINEERING IN SMALL AND MEDIUM ENTERPRISES Prof. Dr Slobodan Stefanović High School of Applied Professional Studies, Vranje, Serbia Prof. Dr Radoje Cvejić Faculty for strategic and operational management Belgrade, Serbia ABSTRACT In economic terms, linear programming is a mathematical technique used for selecting one among more possible economic decisions that will have the greatest efficiency. Most production issues have been solved by a linear programming method, also performed here, and a model of linear programming of economic parameters in re- engineering of small and medium enterprises, for their greater efficiency, is presented. Key words: linear programming, re-engineering, economic parameters, model. 1.0. INTRODUCTION Linear programming is a mathematical method for selecting an optimal solution among larger number of possible solutions. In mathematical terms, linear programming is a mathematical analysis of optimum problem.......

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...Applied mathematics for business, economics, life sciences, and social sciences, 1997, 1175 pages, Raymond A. Barnett, Michael R. Ziegler, Karl Byleen, 0135745756, 9780135745755, Prentice Hall, 1997 Published: 14th July 2010 DOWNLOAD http://bit.ly/1RspljW Applied mathematics for business, economics, life sciences, and social sciences This book prepares readers to understand finite mathematics and calculus used in a wide range of disciplines. Covering relevant topics from finance, linear algebra, programming, and probability, the Seventh Edition places emphasis on computational skills, ideas, and problem solving. Other highlights include a rich variety of applications and integration of graphing calculators. Provides optional regression analysis, containing optional examples and exercises illustrating the use of regression techniques to analyze real data. Both graphing calculator and spreadsheet output are included. Offers more optional technology examples and exercises using actual data. Implements use of graphing calculators in optional examples, exercises in technology, illustrations of applications of spreadsheets and sample computer output. DOWNLOAD http://bit.ly/1qC8Dk0 http://www.jstor.org/stable/2483933 Solutions manual to accompany Raymond A. Barnett and Michael R. Ziegler's finite mathematics for business, economics, life sciences, and social sciences , R. Michael Ziegler, Raymond A. Barnett, 1990, Science, 476 pages. . Precalculus functions and......

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...MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics COURSE SYLLABUS 1. Course Code: Math 10-3 2. Course Title: Algebra 3. Pre-requisite: none 4. Co-requisite: none 5. Credit: 3 units 6. Course Description: This course covers discussions on a wide range of topics necessary to meet the demands of college mathematics. The course discussion starts with an introductory set theories then progresses to cover the following topics: the real number system, algebraic expressions, rational expressions, rational exponents and radicals, linear and quadratic equations and their applications, inequalities, and ratio, proportion and variations. 7. Student Outcomes and Relationship to Program Educational Objectives Student Outcomes Program Educational Objectives 1 2 (a) an ability to apply knowledge of mathematics, science, and engineering √ (b) an ability to design and conduct experiments, as well as to analyze and interpret from data √ (c) an ability to design a system, component, or process to meet desired needs √ (d) an ability to function on multidisciplinary teams √ √ (e) an ability to identify, formulate, and solve engineering problems √ (f) an understanding of professional and ethical responsibility √ (g) an ability to communicate effectively √ √ (h) the broad education necessary to understand the impact of engineering solutions in the global and societal context √ √ (i) a recognition of the need for, and an ability to......

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...Importancia del Álgebra Lineal en la Vida Diaria Adribel González 20143098 El álgebra lineal es vital en múltiples áreas de la ciencia en general. Debido a que las ecuaciones lineales son tan fáciles de resolver, prácticamente todas las áreas de la ciencia moderna contiene modelos en los que las ecuaciones se aproximan mediante ecuaciones lineales y resolviendo el sistema ayuda a desarrollar la teoría. Dado que en la mayoría de los casos, la resolución de ecuaciones es un sinónimo de resolver un problema práctico, esto puede ser muy útil. Sólo por esta razón, el álgebra lineal tiene una razón de ser, y es una razón suficiente para cualquier estudiante aprender álgebra lineal. La informática ha entregado extraordinarios beneficios en las últimos décadas. La amplitud y profundidad de estas aportaciones se están acelerando junto a un mundo que se conecta globalmente. Al mismo tiempo, el campo de la informática tiene como objetivo el tocar casi todas las facetas de nuestras vidas. El álgebra lineal ha jugado un papel importantísimo en estos avances, pues ha permitido que la integración entre las áreas de la matemática sea más simple y eficiente, permitiendo que problemas muy complejos puedan ser divididos e iterados con técnicas relativamente sencillas. En el día a día, con solo encender una computadora, cruzar un puente o usar detergente estamos poniendo en uso el álgebra lineal. Las matrices se utilizan para estudiar cosas como cadenas de Markov, que......

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...The discriminant of x4 + 1 is D = 256 = 28 . We have x4 + 1 ≡ (x + 1)4 (mod 2). Let p be an odd prime (so p D), and suppose the irreducible factors of x4 + 1 have degrees n1 , n2 , . . . , nk . By Corollary 41, the Galois group of x4 + 1 contains an element with cycle structure (n1 , n2 , . . . , nk ). Since the Galois group of x4 + 1 over Q is the Klein 4-group, in which every element has order dividing 2, it follows that each ni = 1 or 2. This gives the possibilities (1, 1, 1, 1), (1, 1, 2), (2, 2). However, D is a square and so the Galois group in contained in A4 ; in particular it contains no transpositions, so (1, 1, 2) is ruled out. This leaves the possibilities (1, 1, 1, 1), and (2, 2), which correspond to the factorization into 4 linear factors or 2 quadratic factors, respectively. Exercise 14.8.3. Proof. The polynomial f (x) = x5 + 20x + 16 is irreducible mod 3 and hence must be irreducible. The Galois group is therefore a transitive subgroup of S5 . The discriminant of f (x) is 216 56 and hence a square; therefore the Galois group is a subgroup of A5 . Modulo 7, we have factorization into irreducibles as f (x) ≡ (x + 2)(x + 3)(x3 + 2x2 + 5x + 5) (mod 7). Therefore the Galois group contains a 3 cycle. From the table on page 643, we see that the Galois group must be isomorphic to A5 . Exercise 14.8.6. Proof. By Eisenstein at 3, we see that f (x) is irreducible, so the Galois group is a transitive subgroup of S5 . The discriminant is 210 34 55 , which is not a square,......

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...LINEAR PROGRAMING AND SIMPLEX METHOD Devharajan Rangarajan Department of Electronic Engineering National University of Ireland, Maynooth devharajan.rangarajan.2016@mumail.ie Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization. This paper focuses on one such optimization technique known as Linear programming and one of its method known as Simplex method in detail with examples. cTx = c1x1 + · · · + cnxn The subject of linear programming can be defined quite concisely. It is concerned with the problem of maximizing or minimizing a linear function whose variables are required to satisfy a system of linear constraints, a constraint being a linear equation or inequality. The subject might more appropriately be called linear optimization. Problems of this sort come up in a natural and quite elementary way in many contexts but especially in problems of economic planning. (or Ax ≤ b) I. INTRODUCTION Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labour, and then determining the "best" production levels for maximal profits under those conditions. In "real life",......

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