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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mywbut.com Operation Research Code: IT504D Contact: 3L + 1T Credits: 4 Module I Linear Programming Problems (LPP): Basic LPP and Applications; Various Components of LP Problem Formulation. Solution of Linear Programming Problems: Solution of LPP: Using Simultaneous Equations and Graphical Method; Definitions: Feasible Solution‚ Basic and non-basic Variables‚ Basic Feasible Solution‚ Degenerate and Nondegenerate Solution‚ Convex set and explanation with examples. [5L] Solution of LPP by Simplex
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Contents Case Problem 2 Case Facts 2 Input Parameters 2 Output Parameters 2 Input Parameters Table 2 Output Parameters Table 3 Additional Case Facts 3 Constraints & Objective Function 3 LP Formulation – For School A 4 Solutions – Excel Solver 5 For School A 5 For School B 5 For School C 6 Solution 6 Conclusion 6 Case Problem Mr Shyam Prasad‚ recently transferred to Chennai from Lucknow‚ has to choose a school for his two children. He has three choices of the school and it is likely that his
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Chapter 3‚ Problem 8 Information from problem 7. Formulate LPM to determine the number of basketballs and footballs to produce in order to maximize profit. X1 -- # of basketballs X2 -- # of footballs Maximize Z = 12x1 + 16x2 Subject to: 3x1 + 2x2 ≤ 500 4x1 + 5x2 ≤ 800 X1‚ x2 ≥ 0 Transform this model to standard form. Maximize Z = 12x1 + 16x2 + 0s1 +0s2 3x1 + 2x2 + s1 = 500 4x1 +5x2 + x2 = 800 X1‚ x2‚ s1‚ s2 ≥ 0 a). Identify the amount of unused resources (slack) at each of
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NORTHEASTERN UNIVERSITY Department of Mechanical and Industrial Engineering Operations Research Prof. Gupta OR 6205 Fall 2014 Class Handout No. 1 Problem No. 1. A manufacturing firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them products 1‚ 2‚ and 3. The available capacity on the machines that might limit output is summarized
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Pace University DigitalCommons@Pace Faculty Working Papers Lubin School of Business 11-1-1999 The Mystery of Linear Programming Explained: Second Edition Jack Yurkiewicz Pace University Follow this and additional works at: http://digitalcommons.pace.edu/lubinfaculty_workingpapers Recommended Citation Yurkiewicz‚ Jack‚ "The Mystery of Linear Programming Explained: Second Edition" (1999). Faculty Working Papers. Paper 21. http://digitalcommons.pace.edu/lubinfaculty_workingpapers/21
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MT105a Study Notes – J.Fenech Chapter 1/2 – Basics 1. Basic notations 1.1. Sum of: ∑ 1.2. Product of: ∏ 2. Sets A = {1‚2‚3} describes the set A containing members 1‚ 2‚ and 3. A={n | n is a whole number and 1≤n≤3} x A denotes that x is a member of set A S T denotes that S is a subset of T A B is the set whose members belong to either set A‚ set B or both i.e. A B = {x | x A or x B} A B is the intersection of 2 sets where A B = {x | x A and x B} denotes an empty
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NAME: TIME: 3 hours (180 minutes) PAGES: 20 (including this cover page) INSTRUCTIONS: 1. Total Mark Value: 100 Number of questions: 7 2. 1 page (single-sided-letter-sized) notes are permitted. 3. Stand-alone-non-programmable calculators are permitted. 4. Budget your time carefully. 5. Answers are to be given in the space provided. However‚ should you require additional space for a complete answer‚ use the blank page attached for this purpose. 6. For all problems where calculation space is
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Chapter 9 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. Use the simplex tables to conduct sensitivity analysis 6. Construct the dual problem from the primal problem © 2009 Prentice-Hall
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WRC 1013 Writing Prompt #1 – Artificial Intelligence/Nuclear Power Thesis & Outline: ______________________________ Rough Draft: __________________________________ Final Draft:____________________________________ Option #1: Explain why the authors below do not fear the advent of artificial intelligence. Write an informative essay that focuses primarily on the performance of IBM’s Watson on the quiz show Jeopardy. Feel free to reference a pop culture movie or TV show where artificial intelligence
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