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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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 was used to generate the independent variable. 3
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Chapter 8 Linear Programming Applications To accompany Quantitative Analysis for Management‚ Eleventh Edition‚ Global Edition by Render‚ Stair‚ and Hanna Power Point slides created by Brian Peterson Copyright © 2012 Pearson Education 8-1 Learning Objectives After completing this chapter‚ students will be able to: 1. Model a wide variety of medium to large LP problems. 2. Understand major application areas‚ including marketing‚ production‚ labor scheduling‚ fuel blending‚ transportation‚ and
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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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OBJECTIVES The objective of the experiment was To calibrate a 10 mL volumetric pipette To calibrate a 25 mL volumetric pipette To calibrate a 100 mL volumetric flask To calibrate a 50 mL measuring cylinder INTRODUCTION The purpose of this experiment is to study the relationship of several types of volumetric glassware and the accuracy of measuring the volumes of liquids very precisely in quantitative laboratory work. The accuracy of the measurement the volumes is the degree of closeness
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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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of period “zero”. So the first “future” cash flow accrues at time ..... We use the letter “t” to refer to a “generic” period. “now” “in one year” “in two years” 0 1 2 CF0 CF1 CF2 APR: Annual Percentage Rate. EAR: Expected A Rate. For simplicity‚ we will assume that all cash flows accrue at the very end of a “period”. That is unrealistic‚ but it simplifies things a bit. Easy to adapt calculations where needed (using spreadsheets) Some asset pricing tools
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5 5 5 Compute: ATB(3 marks) tr (AB)(1 mark) (e) Determine if (2‚ -1) is in the set generated by = (3‚ 1)‚ (2‚ 2) (5 marks) Question Two (20 marks) Let T: R2 R2 be defined by T(x‚ y) = (x + y‚ x). Show that T is a linear transformation.(7 marks) Find the basis and dimension of the row space of the matrix.(6 marks) 2 -1 3 A= 1 1 5 -1 2 2 Compute A-1 using row reduction method.(7 marks) 1 4 3 A= -1 -2 0 2
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Table Z: Areas under the standard normal curve (negative Z) Second decimal place in z 0.06 0.05 0.04 0.03 0.09 0.08 0.07 0.02 0.01 0.0001 0.0001 0.0002 0.0002 0.00 * 0.0000 0.0001 0.0001 0.0002 0.0002 z -3.9 -3.8 -3.7 -3.6 -3.5 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0
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Thank You for Your Service It’s almost four o’clock in northern Maine on a cool spring morning. Bags are rustling and seat-belts are unbuckling as everyone starts to get out of their seats and into the isle‚ waiting impatiently‚ to stand on American soil once again. While walking into an empty airport terminal‚ one by one‚ with a bag over our shoulders and rifle in hand‚ the muffled sounds of clapping starts to hit our ears. Nearing the opening between terminals the vibrating sounds of clapping
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