this purpose it should either produce materials locally or purchase them from another textile firm or doing both actions . Table 1 : Production rates of suit materials Table 2 : Demand ‚ selling and purchase prices ‚ production cost (The linear programming model related to this maximization problem is expressed in 3 variables) S = super machine ; R = regular machine ; P = purchasing price Decision variables : S1 = number of Material type 1 manufactured by the super machines S2 = number of Material
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Lecture 6 GOAL PROGRAMMING INTRODUCTION In many important real-world decision-making situations‚ it may not be feasible‚ or desirable to reduce all the goals of an organization into b. single objective. For example‚ instead of focusing only on optimizing profits‚ the organization may simultaneously be interested in maintaining a stable work force‚ increasing its share of market and limiting price increases. Goal programming is an extension of linear or nonlinear programming involving an objective
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that any content on such websites is‚ or will remain‚ accurate or appropriate. For Anna‚ Nicholas‚ and Nora Dani¨l and Margriet e Contents Preface 1 Introduction 1.1 Mathematical optimization . . . . . . 1.2 Least-squares and linear programming 1.3 Convex optimization . . . . . . . . . . 1.4 Nonlinear optimization . . . . . . . . 1.5 Outline . . . . . . . .
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Assignment 1 (Individual Assignment) 25% Marks Due date: 9 July 2012 (no word limit) Case Study: Scottsville Textile Mill _________________________________________________________ This task will relate to analytical skills in solving optimisation problem (linear programming) using Excel with Solver add-in. Scottsville Textile Mill1 1 Case from Anderson‚ D.‚ Sweeney D.‚ Williams T.‚ Martin‚ K. (2010)‚ An Introduction to Management Science Quantitative
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References: Bradley‚ S. P.‚ A. C. Hax‚ T. L. Magnanti. 1977. Applied Mathematical Programming. Addison-Wesley‚ Reading‚ MA. Hillier‚ F. S.‚ G. J. Lieberman. 2004. Introduction to Operations Research‚ 8th ed. McGraw Hill‚ Boston. Talluri‚ K.‚ G. van Ryzin. 2004. The Theory and Practice of Revenue Management. Kluwer‚ Boston. Tuck School of
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REVISED M09_REND6289_10_IM_C09.QXD 5/12/08 12:01 PM Page 115 9 C H A P T E R Linear Programming: The Simplex Method TEACHING SUGGESTIONS Teaching Suggestion 9.1: Meaning of Slack Variables. Slack variables have an important physical interpretation and represent a valuable commodity‚ such as unused labor‚ machine time‚ money‚ space‚ and so forth. Teaching Suggestion 9.2: Initial Solutions to LP Problems. Explain that all initial solutions begin with X1 ϭ 0‚ X2 ϭ 0 (that
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Julia’s Food Booth. Parts A thru C. Please provide linear programming model‚ graphical solution‚ sensitivity report‚ and answers to questions A thru C. (Problem on page 2) [pic] [pic] A) Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. Let‚ X1 =No of pizza slices‚ X2 =No of hot dogs‚ X3 = barbeque sandwiches Formulation: 1. Calculating Objective function co-efficients:
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Ye Department of Management Science and Engineering Stanford University Stanford‚ CA 94305‚ U.S.A. http://www.stanford.edu/˜yyye (LY‚ Chapters 2.3-2.5‚ 3.1-3.4) Yinyu Ye‚ MS&E‚ Stanford MS&E310 Lecture Note #05 2 Geometry of linear programming Consider maximize subject to x1 x1 +2x2 ≤1 x2 ≤1 ≤ 1.5 ≥ 0. +x2 x2 x1 x1 ‚ Yinyu Ye‚ MS&E‚ Stanford MS&E310 Lecture Note #05 3 LP Geometry depicted in two variable space If the direction of c is contained by the norm
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Bibliography: 1. Bartle‚ Robert G. and Sherbert‚ Donald R. 1992: Introduction to Real Analysis‚ Wiley‚ New York. 3. Bazaraa‚ M. S. 1993: Nonlinear Programming‚ Wiley‚ New York. 4. Berberian‚ Sterling K. 1994: A First Course in Real Analysis‚ Spnnger-Verlag‚ New York. 5. Bertsekas‚ Dmiitri P. 1976: Dynamic Programming and Stochastic Control‚ Academic Press‚ New York. 8. Browder‚ Andrew‚ Halmos‚ P. R. and Axler‚ S. 1996: Mathematical Analysis: An Introduction‚ Springer Verlag‚ New
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MERTON TRUCK COMPANY Sol 1 : Given : Selling Price od Model 101 truck : 39000 Selling Price of Model 102 truck : 38000 We know‚ Contribution C = SP – VC VC for Model 101 : Direct Material + Direct Labor + Variable Overhead : 24000 + 4000 + 8000 = $36000 VC for Model 102: Direct Material + Direct Labor + Variable Overhead : 20000+ 4500+8500 = $33000 Let no of Model 101 produced be X Let no of Model 102 produced be Y Z= (39000-36000)X + (38000=33000)Y Z=3000X + 5000Y
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