...Algebra 1: Simplifying Algebraic Expressions Lesson Plan for week 2 Age/Grade level: 9th grade Algebra 1 # of students: 26 Subject: Algebra Major content: Algebraic Expressions Lesson Length: 2 periods of 45 min. each Unit Title: Simplifying Algebraic Expressions using addition, subtraction, multiplication, and division of terms. Lesson #: Algebra1, Week 2 Context This lesson is an introduction to Algebra and its basic concepts. It introduces the familiar arithmetic operators of addition, subtraction, multiplication, and division in the formal context of Algebra. This lesson includes the simplification of monomial and polynomial expressions using the arithmetic operators. Because the computational methods of variable quantities follows from the computational methods of numeric quantities, then it should follow from an understanding of basic mathematical terminology including the arithmetic operators, fractions, radicals, exponents, absolute value, etc., which will be practiced extensively prior to this lesson. Objectives • Students will be able to identify basic algebraic concepts including: terms, expressions, monomial, polynomial, variable, evaluate, factor, product, quotient, etc. • Students will be able to simplify algebraic expressions using the four arithmetic operators. • Students will be able to construct and simplify algebraic expressions from given parameters. • Students will be able to evaluate algebraic expressions. • Students...
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...Constructing Formulas for Mathematical Operations in Excel (Basic Tips and Techniques) Michelle A. Applequist Computer Information Systems (CIS105) Professor Hari Dhungana Strayer University September 1, 2009 Constructing Formulas for Mathematical Operations in Excel Microsoft Excel uses formulas to construct mathematical operations in a worksheet. After data have been entered into the worksheet, you can perform calculations, analyze data, and create charts. An Excel formula (calculations you create) and functions (formulas pre-existing in Excel) calculates the data entered in the worksheet. Formulas calculate numbers in a particular order. “Excel has one of the most comprehensive set of formulas, not only to perform calculations but also to manage data and records. It also has the ability to instantaneously re-calculate the results as the raw data changes” (Khoo, 2006-9, para. 2). To construct a formula after you have entered data, you must click in the cell that you want the results to appear in, and then type the formula. You can construct formulas by using the sum function, and editing numbers in a cell. It is stated that: Sum is an Excel function—a prewritten formula. Sum indicates the type of calculation that will take place (addition). When the sum function is activated, Excel looks above the active cell for a range of cells to sum. If there is no range above the cell, Excel will look to the left for a range of cells to...
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...Mathematical Operations of Numbers and Simplifying Algebraic Expressions Section A.: Mathematical Operations of Numbers 1.) 8+((12+5) x 4)/2= 8+(17x4)/2= 8+68/2= 8+34= 42 2.) ((3+4)²+4)-2= (7²+4)-2= (49+4)-2= 53-2= 51 3.) ((12+7)+(8/4)²) (19)+(2)² 19+4 23 4.) ½ + ¼ - ⅓= 6/12+3/12-4/12= 9/12-4/12= 5/12 5.) 2/3 x 3/5 = Multiply straight across 2/3 x 3/5 = 6/15 Find common denominator Reduce to lowest term 6/15 ÷ 3/3 = 2/5 6.) ⅓ ÷ ½ = Multiply by reciprocal ⅓ x 2/1= 2/3 7.) 3/2 ÷ ( 1/5 + 6/10) = 3/2 ÷ (2/10 + 6/10) = 3/2 ÷ 8/10 = Multiply by reciprocal 3/2 x 10/8 = 30/16 = 15/8 = 1 7/8 Section B.: Simplifying Algebraic Expressions 1.) 2x + 3x - 5x + x = 5x - 5x + x = 0 + x = x 2.) 2(6x + 5) = 2(6x) + (2x5) = 12x + 10 = 3.) (14x - 7) /7 = 14x - 7 ÷ 7 = 14x ÷ 7 = 2x -7 ÷ 7 = -1 2x - 1 4.) -(-15x) - 3x = 15x - 3x = 12x 5.) 5(3x+4) - 4 = 15x + 20 - 4 = 15x + 16 = 6.) 5(3x-2)+12x = 15x -10+12x = 27x - 10 = 7.) 4(2y-6)+3(5y+10) = 8y-24+15y+30 = 23y-24+30 = 23y+6= 8.) (x+1) (x-2) = Multiply the first 2, outside 2, inside 2, last 2 xx - 2x + 1x - 2 = xx - 2x + x - 2...
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...This week’s material is pretty easy to learn. My learning strategy stayed the same from last week; read the reading material, look at the optional video lectures, answer the discussion question, program the programming assignment, take the self-quiz, etc. … I appreciate learning about the for … each loop. I’m plenty familiar with the for loop, which iterates for a set number of loops, uses initialization, a continue condition, and updating at the top of its block; but, the for … each control structure is a alternative to for. The for .. each loop control structure does not have as complicated continue conditions, and iterates the length of the data structure. I want to master the for .. each loop because it processes a data structure better then the for loop. I interacted with people in the discussion forum. This week’s question asked students to detail the for , and for … each control structure, and include the enum data structure in the explanation. I posted a discussion post, complete with programming examples of each data structure, but there are not enough other student responses to assess. I’ll keep looking for other students to post their discussion assignment, as I need to assess three student discussion posts. This week, I feel it will be helpful to master the for .. each, while, and do … while control structures. Often, I use the for loop, and select case / switch, but the other loops escape my programming toolbox. This week, I learned how to program with while...
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...Aaron Sura June 2, 2014 Wiley plus exercise Question 1. (a). $181,500 (b). $41,200 (c). 38,000 (d). 19,200 (e). 9,500 (f). 63,400 Question 3. In its first month of operation, Maze Company purchased 100 units of inventory for $6, then 200 units for $7, and finally 150 units for $8. At the end of the month, 180 units remained. Compute the amount of phantom profit that would result if the company used FIFO rather than LIFO. The company uses the periodic method. FIFO: $1,410 150 units multiplied by $8 equals $1,200 30 units multiplied by $7 equals $210 $1,200 plus $210 equals $1,410 LIFO: $1,160 100 units multiplied by $6 equals $600 80 units multiplied by $7 equals $560 $600 plus $560 equals to $1,160 Therefore, the phantom profit would be $250 if the company were to use the FIFO rather than LIFO. Question 4. Compute the lower of cost or market valuation for O'Connor's inventory. 12,500(camera)+9,000(camcorders)+12,800(DVD’s)= $34,300 Question 5. Establishment of responsibilities: Only cashiers may operate registers. Segregation of duties: The duties of receiving cash, recording cash, and having custody of cash are assigned to different individuals. Independent and internal verifications: Daily cash counts are made by cashier department supervisors. Human resource control: All cashiers are bonded Physical controls: All over-the-counter receipts are registers. Question 6. Segregation of duties: 3 Establishment of responsibilities:...
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...yDylan Dissanayake Student ID : 15223568 Session 1 : Earth Buddy 10/01/12 Q1. How many Earth Buddies can Ben count on producing in one shift? How many if the factory works 2 shifts? Three shifts? How many if it operates three shifts a day, seven days a week? Which operation is the bottleneck? TASK | TIME | NUMBER OF OPERATORS | a.BUDDIES/HR | b.BUDDIES/SHIFT | c.BUDDIES/ "2" SHIFTS | d.BUDDIES/ "3" SHIFTS | e.BUDDIES/ "3" SHIFTS - 7 DAYS | FILLING | 1.5 | 6 | 240 | 1680 | 3360 | 5040 | 35280 | MOULDING | 1.6 | 3 | 225 | 1575 | 3150 | 4725 | 33075 | EYES | 1.2 | 2 | 300 | 2100 | 4200 | 6300 | 44100 | EYE GLASS | 1.2 | 1 | 300 | 2100 | 4200 | 6300 | 44100 | PAINTING | 1.5 | 1 | 240 | 1680 | 3360 | 5040 | 35280 | PACKING | 1.98 | 2 | 363 | 2541 | 5082 | 7623 | 53361 | a. Buddies/hr = 60minutes x Operators time/task b. Buddies/shift = 60minutes x Operators x Productive hrs time/task c. Buddies/ 2 shifts = 60minutes x Operators x Productive hrs x No. Of Shifts time/task d. Buddies/ 3 shifts = 60minutes x Operators x Productive hrs x No. Of Shifts time/task e. Buddies/ 3 shifts = 60minutes x Operators x Productive hrs x No. Of Shifts x Days 7 Days time/task Bottleneck = Lowest output (Moulding) Theoretical Capacity/hr = Operators x 60min ...
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...the Math Programming add-in is installed, several new command lines are added to the OR_MM menu. The menu items under the title Math Programming create models of the different types. Selecting an item from this list causes a dialog box to be presented which constructs a mathematical programming model. The models created by the add-in are solved with the Excel Solver, the Jensen Network Solver or the Jensen LP/IP Solver. All are Excel add-ins. Documentation for these programs can be reached by clicking the links on the lower left. The Solver add-in comes with Excel, and it can solve linear programming, integer programming and nonlinear programming models. The Math Programming add-in automatically builds Solver models and calls the computational procedures that solve the problems. All four model types can be can be solved in this way. The Jensen LP/IP Solver solves linear or integer programming problems. It is available for the Linear/Integer Programming and Network Flow Programming model types. The Jensen Network Solver can solve pure or generalized network flow models. Both linear and integer problems can be solved. It is available for the Network Flow Programming or Transportation model types. Parametric analysis can be applied to any of the math programming models. Here one parameter is allowed to vary within a specified range and the model is solved for each value. The results are provided by a table and a chart. Side Models provide an additional form on which math programming...
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...Prealgebra 1 Samantha Miller Mrs. Kenzora Sometimes putting things in order isn’t all that important. Take a cook’s/chef’s recipe for example, it assures that the recipe will be consistent, but if other cooks/chefs were to use the recipe they would probably get similar results. The order in which a recipe is followed, the way ingredients are mixed and added makes all the difference in the world. The way they put their pots and pans back after a thorough washing probably doesn’t make any difference at all, compared to how they follow a recipe. While looking at a recipe the cooks/chefs are following an order of operations. In math everyone has learned to follow Please Excuse My Dear Aunt Sally which shows us how to solve certain math problems. Please Excuse My Dear Aunt Sally shows us how to solve the problem. The first step in solving the problem is to solve what is in Parenthesis then we move on to Exponents, then Multiplication, Division, Addition, then finally Subtraction. An example of a problem that uses these steps is as follows: 52 – 6 / 2 + 34+ 7 x (12 – 10) First we would solve (12 – 10) because it’s in the parenthesis our answer would be 2, the problems now looks like this 52 – 6 / 2 + 34 + 7 x 2. The next step would be to solve the problems that have exponents which are 52 and 34 the answers to those are 52 = 25 (5 x 5) and 34 = 81 (3 x 3 x 3 x 3) so now the problem looks like this 25 – 6 / 2 + 81 +...
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... MARKETING, AND ENTREPRENEURSHIP SYLLABUS MANAGEMENT 6 PRODUCTION AND OPERATIONS MANAGEMENT I. TITLE OF THE COURSE: Management 6 II. COURSE DESCRIPTIVE TITLE: Production and Operations Management III. COURSE CREDIT: Three (3) units IV. PRE-REQUISITE: Mgmt 1 and Math 4C V. COURSE DESCRIPTION: As a primary business function, along with marketing and finance, the production operations function plays a vital role in achieving the organization’s basic purpose for existence – to satisfy customer needs – by transforming resources into goods and services. Production operations management is important for two reasons: (1) it is the operations function that is primarily concerned with the production of goods and the provision of services, and (2) the operations function typically involves the greatest portion of the organization’s human resources and is responsible for a large portion of the firm’s capital assets. This course introduces the strategic and tactical decisions involved in production operations management. It focuses on the concepts and tools that are used in making decisions as well as trends and global best practices related to the planning and design, operation, and control of production operations systems. VI. COURSE OBJECTIVES: 1. To enable the students to develop a comprehensive understanding of the production/operations function and to appreciate its role as well as its interdependence with the other...
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...ChApter 18 Management of Waiting Lines Teaching Notes Some of the math and calculations can be left out in order to focus more clearly on the concepts of waiting lines. For example, all infinite source problems, including single channel (except constant service time) can be handled using the infinite source queuing table. In the past, queuing presented students with a good bit of computational requirements, and because of that, students frequently lost sight of the underlying concepts. With less emphasis on math of calculations, students can handle individual problems more quickly, allowing an instructor to assign a greater number of homework problems, and hopefully enabling students to enrich their experience with queuing vis a vis a variety of (short) problems. If you want to shorten the material somewhat, I would suggest omitting the finite source model and/or the multiple priority model. You can shorten the section even more by not assigning problems which require cost comparisons, although I personally feel that cost comparisons are perhaps the ultimate goal in an operations management course. Answers to Discussion and Review Questions 1. Queuing analysis is appropriate in analyzing capacity when service and/or arrival rates are highly variable. 2. Variations in service and/or arrival rates create instances in which demand temporarily exceeds capacity. 3. Commonly used measures of system performance include the average number waiting and average time they wait...
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...What is Operations Management? 2013 Joshua Richards POM 343 Due: 12/11/2013 Table of Contents Tale of Things to Come 1 Conceptual Model 2 Class Two: What is Operations Management / Productivity, Competitiveness & Strategy 3 Class Three: Forecasting, Aggregate Planning, MRP and ERP 4 Class Four: Product and Service Design 5 Class Five: Capacity Planning, Process Selection and Facility Layout 6 Class Six: Design of Work Systems and Learning Curves 7 Class Eight: Location Planning and Analysis 8 Class Nine: Management of Quality and Quality Control 9 Class Ten: Inventory Management 10 Class Eleven: JIT and Lean Operations 11 Class Twelve: Supply Chain Management 12 Conclusion 13 Tale of Things to Come I am going to take you on a whirlwind of wonder and learning all based around operations management. At least that is what I saw it as. Coming in to a class with no expectations, mainly because I have never heard of the topic, I was pleasantly surprised. Coming from a person who has hopes and dreams to own or at least run a successful company someday this class had a plethora of information that I will hopefully someday have the opportunity to use. I decided to break the class down week by week. The reason I chose to do this is partly because of the material and partly because of the teaching method. One thing I loved about the class is that as you go along you always continue to use the stuff you learned previously. When we were doing supply...
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...OPERATION RESEARCH Credits: 4 SYLLABUS Development Definition, Characteristics and phase of Scientific Method, Types of models. General methods for solving operations research models. Allocation: Introduction to linear programming formulation, graphical solution, Simplex ethod, artificial variable technique, Duality principle. Sensitivity analysis. Transportation Problem Formulation optimal solution. Unbalanced transportation problems, Degeneracy. Assignment problem, Formulation optimal solution, Variation i.e., Non-square (m x n) matrix restrictions. Sequencing Introduction, Terminology, notations and assumptions, problems with n-jobs and two machines, optimal sequence algorithm, problems with n-jobs and three machines, problems with n-jobs and m-machines, graphic solutions. Travelling salesman problem. Replacement Introduction, Replacement of items that deteriorate with time – value of money unchanging and changing, Replacement of items that fail completely. Queuing Models M.M.1 & M.M.S. system cost considerations. Theory of games introduction, Two-person zero-sum games, The Maximum –Minimax principle, Games without saddle points – Mixed Strategies, 2 x n and m x 2 Games – Graphical solutions, Dominance property, Use of L.P. to games, Algebraic solutions to rectangular games. Inventory Introduction, inventory costs, Independent demand systems: Deterministic models – Fixed order size systems – Economic order quantity (EOQ) – Single items, back ordering...
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...constraints. In these problems, we find the optimal, or most efficient way of using limited resources to achieve the objective of the situation. Linear Programming enables users to model large and complex problems and solve in a short amount of time by the use of effective algorithm, hence it is a powerful and widely used tool in various fields such as science, industrial engineering, financial planning and management decision making. Nowadays, with the development of technology, most of the real world Linear Programming problems are solved by computer programs. Excel Solver is a popular one. We work through different examples to demonstrate the applications of linear Programming model and the use of Excel Solver for various decision making in operation and supply chain management. Components of Linear Programming model To solve the linear programming problems, we first need to formulate the mathematical description called a mathematical model to represent the situation. Linear programming model usually consists of the following components * Decision variables: These represent the choices that the decision maker can control. For example, the number of items to produce, amounts of money to invest in and so on. The decisions variables are represented using symbols such as X1, X2, X3, ….Xn. * Objective function: The objective of the problem is expressed as a mathematical expression in decision variables. The objective may be maximizing the profit, minimizing...
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...Natural Computing Series Series Editors: G. Rozenberg Th. Bäck A.E. Eiben J.N. Kok H.P. Spaink Leiden Center for Natural Computing Advisory Board: S. Amari G. Brassard K.A. De Jong C.C.A.M. Gielen T. Head L. Kari L. Landweber T. Martinetz Z. Michalewicz M.C. Mozer E. Oja G. P˘ un J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel C. Torras a D. Whitley E. Winfree J.M. Zurada For further volumes: www.springer.com/series/4190 Franz Rothlauf Design of Modern Heuristics Principles and Application Prof. Dr. Franz Rothlauf Chair of Information Systems and Business Administration Johannes Gutenberg Universität Mainz Gutenberg School of Management and Economics Jakob-Welder-Weg 9 55099 Mainz Germany rothlauf@uni-mainz.de Series Editors G. Rozenberg (Managing Editor) rozenber@liacs.nl Th. Bäck, J.N. Kok, H.P. Spaink Leiden Center for Natural Computing Leiden University Niels Bohrweg 1 2333 CA Leiden, The Netherlands A.E. Eiben Vrije Universiteit Amsterdam The Netherlands ISSN 1619-7127 Natural Computing Series ISBN 978-3-540-72961-7 e-ISBN 978-3-540-72962-4 DOI 10.1007/978-3-540-72962-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011934137 ACM Computing Classification (1998): I.2.8, G.1.6, H.4.2 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations...
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...Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. Vol. 9, No. 3, May 2009, pp. 169–179 issn 1532-0545 09 0903 0169 informs ® doi 10.1287/ited.1090.0031tn © 2009 INFORMS I N F O R M S Transactions on Education Teaching Note Revenue Management at Harrah’s Entertainment, Inc. Narendra Agrawal Department of Operations and Management Information Systems, Leavey School of Business, Santa Clara University, Santa Clara, California 95053, nagrawal@scu.edu Morris A. Cohen, Noah Gans Operations and Information Management Department, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104 {cohen@wharton.upenn.edu, gans@wharton.upenn.edu} D istribution: To maintain the integrity and usefulness of cases published in ITE, distribution of this teaching note to any other party is prohibited. Please refer interested instructors to ITE for access to the teaching note. Section 1, below, contains the suggested case questions. Section 2 provides some background on the case questions, as well as sample answers. Section 3 systematically walks through HarrahsInstructionSpreadsheet.xls, which is one of the two supporting files1 included in this Teaching Note (TN): HarrahsCaseData.xls—supporting data for the case analysis, which can be distributed to students. HarrahsInstructorSpreadsheet.xls—spreadsheet that includes case data, a bid-price linear program (LP), and a Crystal Ball Simulation...
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