...6-1 The famous Y. S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3am, 7am, 11am, 3pm, 7pm, or 11pm, and each works an 8-hour shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided. Chang’s scheduling problem is to determine how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day’s operation. (Hint: Let Xi equal the number of waiters and busboys beginning work in time period i, where i = 1, 2, 3, 4, 5, 6.) If Chang’s were able to reduce the number of required waiters and busboys by 1 during some period, during which period should they make the reduction? Period | Time | Number of Waiters and Busboys Required | 1 | 3am-7am | 3 | 2 | 7am-11am | 12 | 3 | 11am-3pm | 17 | 4 | 3pm-7pm | 11 | 5 | 7pm-11pm | 12 | 6 | 11pm-3am | 4 | In the QM, Let X1 = Number of waiters and busboys at period 1 Let X2 = Number of waiters and busboys at period 2 Let X3 = Number of waiters and busboys at period 3 Let X4 = Number of waiters and busboys at period 4 Let X5 = Number of waiters and busboys at period 5 Let X6 = Number of waiters and busboys at period 6 Period 1 = 3 Period 2 = 14 Period 3 = 3 Period 4 = 8 Period 5 = 4 Period 6 = 0 Period 1, 3 and 5 drop from total 32 workers to 31 each if any of those 3 periods required minimum is reduce by 1. The period I choose (if have...
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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", linear...
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...Session 13 - Homework Problems Miguel Faundez Chapter 13 13.4 Answers a) The scatter plot shows a positive linear relationship. b) For each increase in shelf space of an additional foot, weekly sales are estimated to increase by $7.40. c) Y=145+7.4X=145+7.4(8)=204.2, or $204.20. 13.5 Answers a) From the scatter diagram, we can see that there exists positive relation between reported and audited magazine. b) The slope, B1=26.724 implies that for a unit increment in number of reported magazines, there will be 26.724 increment in the dependent variable, Audited number of magazines. c) The predicted audited newsstand sales for magazine that report newsstand sales of 400,000(X=400) is audited=0.5718+26.724x400=10690.1718. 13.16 Answers a) 20,535/30,025=0.684. 68.4% of the variation in sales can be explained by the variation in shelf space. b) √9,490/10=30.8058. c) Based on a) and b), the model should be useful for predicting the labor hours. 13.17 Answers a) r2 = 130,301.41/144,538.64 = .901498796 This means that 90.15% of the variation in audited sales is explained by the variability in reported sales. b) Formula = SST = SSR + SSE SST-SSR = SSE 144.538.64 – 130,301.41 = 14,237.23 SSE = 14,237.23 SYX = √SSE/ (n – 2) = √14,237.23/ (10 – 2) = √1779.65 SYX = 42.1859 c) This regression model is very helpful in predicting audited sales 13.24 Answers a) A residual analysis of the data indicates a pattern, with sizable clusters of...
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...Unit Four – Case Analysis 1) Describe the primary system described in the story including the parts of the system, the system’s purpose, and the larger system in which it is embedded. The primary system described in The Tip of the Iceberg involved an iceberg, penguins, walruses, and clams. The penguins were living on an iceberg which had a clam bed beneath it. The penguins did not have the tools (sufficient lung capacity or tusks) to crack open the clams, but the walruses did. The walruses were respectful of the penguins’ territory and were not going to access the penguins’ clams without their permission. The penguins had an idea to ask the walruses to harvest the clams for them and in return the walruses could eat clams alongside them as long as they don’t eat the penguins. As more penguins heard of this treaty and made their way to the iceberg more walruses were needed to meet the demand. The system was looped; as more penguins arrived, more clams were needed, and thusly more walruses were also needed. Due to the increase weight of the penguins and walruses, the iceberg began to sink causing the capacity of the iceberg to decrease. The decrease in area resulted in penguins being sat on which lead to fighting amongst the groups. Such fighting makes the appeal of the iceberg decrease which brings the loop back to the number of penguins and walruses wanting clams and iceberg access. Ultimately, the entire penguin, walrus, clam, and iceberg system is part of a larger system...
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...it would mean to a manager (AIU Online). Introduction Regression analysis can help us predict how the needs of a company are changing and where the greatest need will be. That allows companies to hire employees they need before they are needed so they are not caught in a lurch. Our regression analysis looks at comparing two factors only, an independent variable and dependent variable (Murembya, 2013). Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.018314784 R Square 0.000335431 The portion of the relations explained Adjusted R Square -0.009865228 by the line 0.00033% of relation is Standard Error 1.197079687 Linear. Observations 100 ANOVA df SS MS F Significance F Regression 1 0.04712176 0.047122 0.032883 0.856477174 Residual 98 140.4339782 1.433 Total 99 140.4811 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 4.731133588 1.580971255 2.992549 0.003501 1.593747586 7.86852 Intrinsic -slope 0.055997338 0.308801708 0.181338 0.856477 -0.5568096 0.668804 Line equation is benefits =4.73 + 0.0559 (intrinsic) Intercept- t-stat HO: Coefficients is zero. Intrinsic t-stat is zero...
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...Michelle D. Griner MAT540 – Professor Johnson Strayer University Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Formulate the model for the first home game. Explain how you derived the profit function and constraints and show any calculations that allow you to arrive at those equations. Let, X1 =No of pizza slices, X2 =No of hot dogs, X3 = No of barbeque sandwiches Objective function co-efficient: The objective is to maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price. For Pizza slice, Cost/slice=$4.5/6=$0.75 | X1 | X2 | X3 | SP | $1.50 | $1.60 | $2.25 | -Cost | $0.75 | $0.50 | $1.00 | Profit | $0.75 | $1.10 | $1.25 | Maximize Total profit Z = $0.75X1 + 1.10X2 +1.25X3 * Constraints: 1. Budget constraint: 0.75X1 + 0.50X2 + 1.00X3 ≤ $1500 2. Space constraint: Total space available = 3*4*16=192 sq feet =192*12*12=27,648 sq. in. The oven will be refilled during half time. Thus, the total space available = 2*27,648 = 55,296 sq. in. Space required for a pizza = 14*14 = 196 sq. in. Space required for a slice of pizza = 196/6 = 32.667 sq. in. approximately. Thus, space constraint can be written as: 33X1 + 16X2 +25X3 ≤ 55,296 (sp. in of oven space) 3. at least as many slices of pizza as hot dogs and barbeque sandwiches combined X1 ≥ X2 + X3 (at least as many slices of pizza as hot dogs and barbeque sandwiches ...
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...Forecasting Methods Genius forecasting - This method is based on a combination of intuition, insight, and luck. Psychics and crystal ball readers are the most extreme case of genius forecasting. Their forecasts are based exclusively on intuition. Science fiction writers have sometimes described new technologies with uncanny accuracy. There are many examples where men and women have been remarkable successful at predicting the future. There are also many examples of wrong forecasts. The weakness in genius forecasting is that its impossible to recognize a good forecast until the forecast has come to pass. Some psychic individuals are capable of producing consistently accurate forecasts. Mainstream science generally ignores this fact because the implications are simply to difficult to accept. Our current understanding of reality is not adequate to explain this phenomena. Trend extrapolation - These methods examine trends and cycles in historical data, and then use mathematical techniques to extrapolate to the future. The assumption of all these techniques is that the forces responsible for creating the past, will continue to operate in the future. This is often a valid assumption when forecasting short term horizons, but it falls short when creating medium and long term forecasts. The further out we attempt to forecast, the less certain we become of the forecast. The stability of the environment is the key factor in determining whether trend extrapolation is an appropriate forecasting...
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...MODELS FOR ESTIMATION OF ISOMETRIC WRIST JOINT TORQUES USING SURFACE ELECTROMYOGRAPHY by Amirreza Ziai B.Eng., Sharif University of Technology, Tehran, 2008 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In the School of Engineering Science Faculty of Applied Science © Amirreza Ziai 2011 SIMON FRASER UNIVERSITY Summer 2011 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for Fair Dealing. Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. APPROVAL Name: Degree: Title of Thesis: Amirreza Ziai M.A.Sc Models for estimation of isometric wrist joint torques using surface electromyography Examining Committee: Chair: Parvaneh Saeedi, P.Eng Assistant Professor – School of Engineering Science ______________________________________ Dr. Carlo Menon, P.Eng Senior Supervisor Assistant Professor – School of Engineering Science ______________________________________ Dr. Shahram Payandeh, P.Eng Supervisor Professor – School of Engineering Science ______________________________________ Dr. Bozena Kaminska, P.Eng Examiner Professor – School of Engineering Science Date Defended/Approved: _________September 2, 2011 ______________ ii ABSTRACT With an aging...
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...coordinates of the image are (8, -1). Example 2: A rectangle has coordinates (1, 1), (4, 1), (4, 3) and (1, 3). Find the coordinates of the image of the rectangle under the transformation represented by the matrix . Solution: You could find the image of each vertex in turn by finding , etc. However, it is more efficient to multiply the transformation matrix by a rectangular matrix containing the coordinates of each vertex: . So the image has coordinates (2, 0), (11, -3), (9, -1) and (0, 2). The diagram below shows the object and the image: Any transformation that can be represented by a 2 by 2 matrix, , is called a linear transformation. 1.1 Transforming the unit square The square with coordinates O(0, 0), I(1, 0), J(0, 1) and K(1, 1) is called the unit square. Suppose we consider the image of this square under a general linear transformation as represented by the matrix : . We therefore can notice the following things: * The origin O(0, 0) is mapped to itself; * The image of the point I(1, 0) is (a, c), i.e. the first column of the transformation matrix; * The image of the point J(0, 1) is (b, d), i.e. the second column of the transformation matrix; * The image of the point K(1, 1) is (a + b, c+ d), i.e. the result of finding the sum of the entries in each row of the matrix. Example: Find the image of the...
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...Churn Prediction Vladislav Lazarov vladislav.lazarov@in.tum.de Technische Universität München Marius Capota Technische Universität München mariuscapota@yahoo.com ABSTRACT The rapid growth of the market in every sector is leading to a bigger subscriber base for service providers. More competitors, new and innovative business models and better services are increasing the cost of customer acquisition. In this environment service providers have realized the importance of the retention of existing customers. Therefore, providers are forced to put more efforts for prediction and prevention of churn. This paper aims to present commonly used data mining techniques for the identification of churn. Based on historical data these methods try to find patterns which can point out possible churners. Well-known techniques used for this are Regression analysis, Decision Trees, Neural Networks and Rule based learning. In section 1 we give a short introduction describing the current state of the market, then in section 2 a definition of customer churn, its’ types and the imporance of identification of churners is being discussed. Section 3 reviews different techniques used, pointing out advantages and disadvantages. Finally, current state of research and new emerging algorithms are being presented. given a huge choice of offers and different service providers to decide upon, winning new customers is a costly and hard process. Therefore, putting more effort in keeping churn low has become...
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...which can be described by a probability distribution. Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable:[1] see correlation does not imply causation. A large body of techniques for carrying out regression analysis has been developed. Familiar methods such as linear regression and ordinary least...
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...Section 9-1 1. Identify each type of filter response in Figure 9-32. A)Band-pass B)High-pass C)Low-pass D)Band-stop 2. A certain low-pass filter has a critical frequency of 800 Hz. What is its bandwidth? For this low-pass filter with fc of 800 Hz, the bandwidth is 800Hz. 3. A single-pole high-pass filter has a frequency-selective network with R=2.2 kΩ and C=0.0015µF. What is the critical frequency? fc=1/2πRC=1/(2π(2200Ω)(.0000000015F))= 48.2kHz Can you determine the bandwidth from the available information? No. 4. What is the roll-off rate of the filter described in Problem 3? As a single-pole filter it has a roll-off rate of -20 dB\decade. 5. What is the bandwidth of a band-pass filter whose critical frequencies are 3.2 kHz and 3.9 kHz? BW=fc2-fc1=3.9kHz-3.2kHz=700Hz What is the Q of this filter? Q=fo/BW= √fc1fc2/700Hz= √(3.2×3.9)/700=5.05 6. What is the center frequency of a filter with a Q of 15 and a bandwidth of 1 kHz? Q=fo/BW 15= fo/1kHz=15kHz Section 9-2 7. What is the damping factor in each active filter shown in Figure 9-33? DF=2-R1/R2 a)2- 1.2/1.2=1 b)2- 560/1000=1.44 c)both stage 1&2: 2- 330/1000=1.67 Which filters are approximately optimized for a Butterworth response characteristic? b)2- 560/1000=1.44 8. For the filters in Figure 9-33 that do not have a Butterworth response, specify the changes necessary to convert them to Butterworth responses...
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...Marketing Research Fall 2011 Exercise: SPSS 5. Hypothesis test The MBA programme leader is interested to know if there is any significant average age difference between males and females and if there is which is the older group. a. Suggest a null hypothesis and an alternative hypothesis for testing the mean age for male and female students. μ0: The average ages of males and females are the same. μ1: The average ages of males and females are not the same. b. Carry out an appropriate test to compare the mean age for the two sexes, and interpret your results. Since the goal is to compare two means and that the data is of ratio scale, One-Way ANOVA is the appropriate test. Here we have gender as the factor and age as the dependent variable, and we choose the common 0.05 level of significance. Figure 5.1 is the resulting ANOVA table. | | | | | | |3.131a |2 |.209 | | |3.433 |2 |.180 | | |.543 |1 |.461 | | |40 | | | Figure 6.1 Cross table of satisfaction and sex at α=0.05 The p-value, which is 0.209, is very obviously greater than our chosen level of significance, 0.05. The null hypothesis...
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...Applying Time Series Methodologies Derek Griffin RES/342 March 22, 2012 Olivia Scott Applying Time Series Methodologies MEMO To: Myra Reid, VP of Production From: Derek Griffin, Market Analyst Date: 22 March 2012 Subject: Three Week Analysis Simulation to Predict Blues Inc. Forecast Message: Over the past three weeks an indebt research analysis was conducted to provide Blues Inc reasonably accurate forecast that will ensure continued growth to the six percent market share of a 45 billion dollar industry. In week one the marketing team was given a directive from the Chief Executive Officer, Barbara Baderman, to have an effective advertising strategy in place to become the industry leader. A regression analysis was performed using sales as the selected variable for the strong positive relationship to advertising budget. The correlation coefficient of sales with the advertising budget is 0.96, which was higher than the relationship of competitors advertising budget or retail coverage. Sales with a lower standard error indicate a better predicted forecast. Using the regression equation and expected sales of 2,400 million, the forecasted advertising budget should be set at 162 million. During week two the marketing team was challenged to predict the market sales for the next year. Denim sales have increased five percent over the past four years and is expected to increase again next year. The team used the weighted moving average with a weight of .9 for the...
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...ENCODER Documentation A0001229 Rev 1.3, Aug 2011 101 0100101010100000010101010100010101010010101000100010101011111110010100001010100100101010001010101010100101010101001010 0001010101001010100010001010101111111001010000010010100101010010101010000001010101010001010101001010100100100101010010010010 IMPIKA - 135 rue du Dirigeable - 13400 Aubagne - France Tel : + 33 (0)4 42 62 43 00 Fax : + 33 (0)4 42 62 42 99 www.impika.com IMPIKA assumes no responsibility for any errors that may appear in this document. If you have any suggestion for improvements or amendments or have found errors in this publication, please notify us. At the time of publication, this document is intended to be as comprehensive and accurate as possible. However, information contained hereafter can be subjected to modification without prior notice. IMPIKA reserves the rights to modify the features and ESifications of its products without prior notice. This document has been designed by IMPIKA for its customers but also for its internal use. The information contained hereafter is the property of IMPIKA and cannot, under any circumstances, be totally or partially reproduced in any form or by any means including photocopying, without express written permission of IMPIKA. When devices are used for applications with technical safety requirements, the relevant instructions must be followed. Failure to use IMPIKA software or approved software with our hardware products may result in injury, harm, or improper...
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