...Accuracy and precision in the calculation of doses, dosages, and rates of infusion of intravenous solutions are often based on percents, ratios, and proportions. The exercises for this CheckPoint provide opportunities to perform various mathematical functions pharmacy technicians must master. Assume the role of a pharmacy technician. A pharmacist gives you a physician’s order sheet, a prescription, and asks you to prepare a 2% solution of sodium chloride (NaCl). You check the stock in the pharmacy but discover you have only a 3% solution of NaCl. Hint: 2g NaCl:100mL of solution::3g NaCL:x mL of 3% solution. Showall your calculations in a Microsoft® Word document Completethe following exercises. Refer to p. 22 for worked examples. 1. Solve the equation for x to determine how many mL of 3% solution you need. 2. Convert 3% to a fraction. 3. Convert 2% to a decimal. 4. Percents are often used to show the strength of solutions. Which solution is stronger, the 2% or the 3%? 5. What does 3% of sodium chloride mean, i.e., how many parts are in a 100? 6. Referring to the proportion regarding NaCl in the scenario, show the product of the means equals the product of the extremes. 7. Convert 25% to a fraction. 8. What percent of 15 ounces is 5 ounces? 9. Convert 1/8 to a percent. 10. Convert 40% to a decimal. Post your work and answers to all problems along with a signed copy of the Certificate of Originality as an attachment under the Assignment...
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...UNIVERSITY EM 516 – LOGISTICS ASSIGNMENT 4 P-MEDIAN PROBLEM 1892876 - Nurşin ATAK Instructor: Sinan GÜREL December 26th, 2013 ANKARA 1. ABOUT P-MEDIAN PROBLEM: The problem is to locate one or more facilities (sources), such as warehouses, to serve a number of demand points (sinks) of known locations, volumes, and transportation rates. Fixed costs of a candidate set of facilities may also be known. The candidate set of facilities is selected from the demand points. The objective is to find the best P locations from the M candidate sites where P is less than or equal to M. 2. PROBLEM INSTANCE: The problem instance given in PMED01.dat file is considered for comparing Logware method and Linear Programming method. Problem data is taken from PMED01.dat file and demonstrated in Table 1. There are 12 markets being served from up to 5 candidate warehouse locations. The product is shipped over a road network. The annual volumes of the markets, the transportation rates, and the candidate sites with their fixed costs and X&Y Coordinates are shown in Table 1. Point X Y Volume, Transport Rate, No Coordinate Coordinate cwt $/cwt/mi M1 200 100 3000 0,002 M2 500 200 5000 0,0015 M3 900 100 17000 0,002 M4 700 400 12000 0,0013 M5 1000 500 10000 0,0012 M6 200 500 9000 0,0015 M7 200 700 24000 0,002 M8 400 700 14000 0,0014 M9 500 800 23000 0,0024 M10 800 900 30000 0,0011 M11 1200 300 4000 0,0001 M12 200 2000 2000 0,0002 Table 1. Problem Data of 12 Markets Fixed Candidate Cost, $ Sites 200...
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...CHAPTER 1 & 2 1. (Points: 10.0) The people who suggested the wrong solutions in the examples in chapter 1 of the textbook were all ... 1. looking for the easy options. 2. incompetent and unprofessional. 3. lazy people. 4. competent, hard-working professionals. 2. (Points: 10.0) A vision is the ability to see the way things ought to be or will be in the future. True False 3. (Points: 10.0) Finding and solving the real problem is important to minimise lost time, money, and effort. True False 4. (Points: 10.0) Exercising our problem-solving skills frequently will make us better able to ... 1. achieve our goal of choosing the best career. 2. achieve our goal of impressing our bosses. 3. achieve our goal of choosing the best solution. 4. achieve our goal of finding multiple solutions. 5. (Points: 10.0) The textbook lists 7 habits of highly effective people. To 'Synergize' means to ... 1. Aggressively seek new ideas and innovations. 2. Continually review and prioritise your goals. 3. Identify the key issues and results that would constitute a fully acceptable solution to all. 4. Help bring out the best in everyone else. 6. (Points: 10.0) There are things that can be done to guarantee that mistakes will never happen. True False 7. (Points: 10.0) Paradigm pioneers are continually ... 1. searching for ways to impress stakeholders. 2. looking for opportunities to do less...
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...Module B Transportation and Assignment Solution Methods B-1 B-2 Module B Transportation and Assignment Solution Methods Solution of the Transportation Model The following example was used in Chapter 6 of the text to demonstrate the formulation of the transportation model. Wheat is harvested in the Midwest and stored in grain elevators in three different cities—Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each of which is capable of holding one ton of wheat. Each grain elevator is able to supply the following number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis: Grain Elevator 1. Kansas City 2. Omaha 3. Des Moines Total Supply 150 175 275 600 tons Each mill demands the following number of tons of wheat per month. Mill A. Chicago B. St. Louis C. Cincinnati Total Demand 200 100 300 600 tons The cost of transporting one ton of wheat from each grain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. For example, the cost of shipping one ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7. Mill Grain Elevator 1. Kansas City 2. Omaha 3. Des Moines A. Chicago $6 7 4 B. St. Louis $ 8 11 5 C. Cincinnati $10 11 12 The problem is to determine how many tons of wheat to transport from each...
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...of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Library of Congress Cataloging-in-Publication Data Oman, Robert M. Calculus for the utterly confused / Robert M. Oman, Daniel M. Oman. p. cm. ISBN 0-07-048261-6 1. Calculus-Study and teaching. I. Oman, Daniel M. II. Title. QA303.3.043 1998 51 5 4 ~ 2 1 98-25802 CIP Copyright 0 1999 by The...
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...Transportation and Assignment Solution Methods B-1 B-2 Module B Transportation and Assignment Solution Methods Solution of the Transportation Model The following example was used in chapter 6 of the text to demonstrate the formulation of the transportation model. Wheat is harvested in the Midwest and stored in grain elevators in three different cities—Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car capable of holding one ton of wheat. Each grain elevator is able to supply the following number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis. Grain Elevator 1. Kansas City 2. Omaha 3. Des Moines Total Supply 150 175 275 600 tons Each mill demands the following number of tons of wheat per month. Mill A. Chicago B. St. Louis C. Cincinnati Total Demand 200 100 300 600 tons The cost of transporting one ton of wheat from each grain elevator (source) to each mill (destination) differs according to the distance and rail system. These costs are shown in the following table. For example, the cost of shipping one ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7. Mill Grain Elevator A. Chicago B. St. Louis C. Cincinnati 1. Kansas City 2. Omaha 3. Des Moines $6 7 4 $ 8 11 5 $10 11 12 The problem is to determine how many tons...
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...Practice Problems – Osmosis and Water potential Use this key to answer all the problems below. If you choose B or C, rewrite the statement so that it is complete and true. A = TRUE B = FALSE C = NOT ENOUGH INFORMATION PROBLEM ONE: The initial molar concentration of the cytoplasm inside a cell is 2M and the cell is placed in a solution with a concentration of 2.5M. 1. Initially, free energy is greater inside the cell than outside 2. It is possible that this cell is already in equilibrium with its surroundings. 3. Initially, solute concentration is greater outside the cell than inside. 4. Water will enter the cell because solute potential is lower inside the cell than outside. 5. The cell will become flaccid because the pressure potential is greater outside the cell than inside. 6. The cell is already in equilibrium with its surroundings because of the combination of pressure potential and solute potential inside and outside the cell. 7. Initially, the cytoplasm is hypertonic to the surrounding solution. 8. Initially, the numerical value of the solute potential is more negative inside the cell than outside. 9. Net diffusion of water will be from inside the cell to outside the cell. 10. At equilibrium, the molarity of the cytoplasm will have increased. 11. At equilibrium, the pressure potential inside the cell will have increased. PROBLEM TWO: The initial molar concentration of the cytoplasm inside a cell is 1.3 M and the surrounding solution is .3M...
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...TYPICAL SAMPLE PERSUASIVE SPEECH TOPICS 1. abortion 21. drunk driving 2. adoption of children 22. hunger in America 3. cruelty to animals 23. inflation 4. air pollution 24. invasion of privacy 5. air safety 25. juvenile felonies 6. death penalty 26. legalization of drinking at 18 7. Alaskan pipeline 27. prostitution 8. amnesty 28. energy crisis 9. animal shelters 29. euthanasia 10. apartheid 30. reverse discrimination 11. death with dignity 31. sex education 12. auto theft 32. taxes 13. capital punishment 33. gun control 14. care for elderly 34. nuclear waste 15. child abuse 35. ocean pollution 16. cloning 36. oil drilling 17. corruption in public office 37. organ transplants 18. cosmetic surgery 38. unemployment 19. defense budget 39. recycling 20. disarmament 40. pornography EXAMPLES OF CREATIVE PERSUASIVE SPEECH TOPICS 1. I deserve an A on this speech 2. Pete Rose is a Hall of Famer 3. Hooters is a family restaurant 4. David Archuleta should have won American Idol 5. Drink Milk 6. Maxie and Spinelli (General Hospital) belong together 7. Bring Back Crispy M&M’s 8. Change RCC’s priority registration Please come up with a creative topic so I can add it to this list in the future!!! A SPEECH TO PERSUADE (assignment) Speeches to persuade seek...
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...Solutions to old Exam 1 problems Hi students! I am putting this old version of my review for the first midterm review, place and time to be announced. Check for updates on the web site as to which sections of the book will actually be covered. Enjoy!! Best, Bill Meeks PS. There are probably errors in some of the solutions presented here and for a few problems you need to complete them or simplify the answers; some questions are left to you the student. Also you might need to add more detailed explanations or justifications on the actual similar problems on your exam. I will keep updating these solutions with better corrected/improved versions. Problem 1(a) - Fall 2008 Find parametric equations for the line L which contains A(1, 2, 3) and B(4, 6, 5). Solution: To get the parametric equations of L you need a point through which the line passes and a vector parallel to the line. −→ Take the point to be A and the vector to be the AB. The vector equation of L is −→ −→ r(t) = OA + t AB = 1, 2, 3 + t 3, 4, 2 = 1 + 3t, 2 + 4t, 3 + 2t , where O is the origin. The parametric equations are: x = 1 + 3t y = 2 + 4t, z = 3 + 2t t ∈ R. Problem 1(b) - Fall 2008 Find parametric equations for the line L of intersection of the planes x − 2y + z = 10 and 2x + y − z = 0. Solution: The vector part v of the line L of intersection is orthogonal to the normal vectors 1, −2, 1 and 2, 1, −1 . Hence v can be taken to be: i j k v = 1, −2, 1 × 2, 1, −1 = 1 −2 1 = 1i + 3j + 5k. 2 1 −1 Choose P ∈ L so...
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...Problems and Solutions 1 CHAPTER 1—Problems On 12/04/01, consider a fixed-coupon bond whose features are the following: • • 1.1 Problems on Bonds Exercise 1.1 face value: $1,000 coupon rate: 8% • coupon frequency: semiannual • maturity: 05/06/04 What are the future cash flows delivered by this bond? Solution 1.1 1. The coupon cash flow is equal to $40 8% × $1,000 = $40 2 It is delivered on the following future dates: 05/06/02, 11/06/02, 05/06/03, 11/06/03 and 05/06/04. The redemption value is equal to the face value $1,000 and is delivered on maturity date 05/06/04. Coupon = Exercise 1.3 An investor has a cash of $10,000,000 at disposal. He wants to invest in a bond with $1,000 nominal value and whose dirty price is equal to 107.457%. 1. What is the number of bonds he will buy? 2. Same question if the nominal value and the dirty price of the bond are respectively $100 and 98.453%. Solution 1.3 1. The number of bonds he will buy is given by the following formula Number of bonds bought = Cash Nominal Value of the bond × dirty price Here, the number of bonds is equal to 9,306 n= 2. n is equal to 101,562 n= Exercise 1.4 10,000,000 = 101,571.31 100 × 98.453% 10,000,000 = 9,306.048 1,000 × 107.457% On 10/25/99, consider a fixed-coupon bond whose features are the following: • face value: Eur 100 2 Problems and Solutions • • coupon rate: 10% coupon frequency: annual • maturity: 04/15/08 Compute the accrued interest taking into account the four different day-count...
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...simple linear programming problems in terms of an objective function to be maximized or minimized subject to a set of constraints. • find feasible solutions for maximization and minimization linear programming problems using the graphical method of solution. • solve maximization linear programming problems using the simplex method. • construct the Dual of a linear programming problem. • solve minimization linear programming problems by maximizing their Dual. 0.1.2 Introduction One of the major applications of linear algebra involving systems of linear equations is in finding the maximum or minimum of some quantity, such as profit or cost. In mathematics the process of finding an extreme value (maximum or minimum) of a quantity (normally called a function) is known as optimization . Linear programming (LP) is a branch of Mathematics which deals with modeling a decision problem and subsequently solving it by mathematical techniques. The problem is presented in a form of a linear function which is to be optimized (i.e maximized or minimized) subject to a set of linear constraints. The function to be optimized is known as the objective function . Linear programming finds many uses in the business and industry, where a decision maker may want to utilize limited available resources in the best possible manner. The limited resources may include material, money, manpower, space and time. Linear Programming provides various methods of solving such problems. In this unit, we present...
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...Solutions to Case Problems Manual to Accompany An Introduction To Management Science Quantitative Approaches To Decision Making Twelfth Edition David R. Anderson University of Cincinnati Dennis J. Sweeney University of Cincinnati Thomas A. Williams Rochester Institute of Technology R. Kipp Martin University of Chicago South-Western Cincinnati, Ohio Contents Preface Chapter 1: Introduction ♦ Scheduling a Golf League Chapter 2: An Introduction to Linear Programming ♦ Workload Balancing ♦ Production Strategy ♦ Hart Venture Capital Chapter 3: Linear Programming: Sensitivity Analysis and Interpretation of Solution ♦ Product Mix ♦ Investment Strategy ♦ Truck Leasing Strategy Chapter 4: Linear Programming Applications in Marketing, Finance and Operations Management ♦ Planning an Advertising Campaign ♦ Phoenix Computer ♦ Textile Mill Scheduling ♦ Workforce Scheduling ♦ Duke Energy Coal Allocation Chapter 6: Distribution and Network Models ♦ Solution Plus ♦ Distribution Systems Design Chapter 7: Integer Linear Programming ♦ Textbook Publishing ♦ Yeager National Bank ♦ Production Scheduling with Changeover Costs Chapter 8: Nonlinear Optimization Models ♦ Portfolio Optimization with Transaction Costs Chapter 9: Project Scheduling: PERT/CPM ♦ R.C. Coleman Chapter 10: Inventory Models ♦ Wagner Fabricating Company ♦ River City Fire Department Chapter 11: Waiting Line Models ♦ Regional Airlines ♦ Office Equipment, Inc. Chapter 12: Simulation ♦ Tri-State Corporation...
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...Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics A Semester Course in Finite Mathematics for Business and Economics Marcel B. Finan c All Rights Reserved August 10, 2012 1 Contents Preface 4 Mathematics of Finance 1. Simple Interest . . . . . . . . . . . . . . . . . . . . . . . 2. Discrete and Continuous Compound Interest . . . . . . 3. Ordinay Annuity, Future Value and Sinking Fund . . . 4. Present Value of an Ordinay Annuity and Amortization . . . . Matrices and Systems of Linear Equations 5. Solving Linear Systems Using Augmented Matrices . . . . 6. Gauss-Jordan Elimination . . . . . . . . . . . . . . . . . . 7. The Algebra of Matrices . . . . . . . . . . . . . . . . . . 8. Inverse Matrices and their Applications to Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . Linear Programming 9. Solving Systems of Linear Inequalities . . . . . . . . . . . . . . 10. Geometric Method for Solving Linear Programming Problems 11. Simplex Method for Solving Linear Programming Problems . 12. The Dual Problem: Minimization with ≥ Constraints . . . . . Counting Principles, Permuations, and 13. Sets . . . . . . . . . . . . . . . . . . 14. Counting Principles . . . . . . . . . 15. Permutations and Combinations . . . . . . 5 5 12 19 26 . . . . 34 34 42 53 62 . . . . 69 69 77 86 97 Combinations 106 . . . . . . . . . ...
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... Do It! Exercises 1, 2, 3, 4, 5, 6 1 1, 2 1, 2 Record the issuance of ordinary shares. 7, 8, 9, 10, 11 2, 3, 4 3 *3. Explain the accounting for treasury shares. 12, 13, 14 5 4 *4. Differentiate preference shares from ordinary shares. 15 6 *5. Prepare the entries for cash dividends and share dividends. 17, 18, 19, 20, 21, 22 7, 8, 9 *6. Identify the items that are reported in a retained earnings statement. 16, 23, 24 Questions *1. Identify the major characteristics of a corporation. *2. 7. Prepare and analyze a comprehensive equity section. *8. Compute book value per share. B Problems 2, 3, 4, 7, 8, 11, 12 1A, 3A, 6A 1B, 3B 5, 7, 9 11, 12 2A, 3A, 6A 2B, 3B 6, 7, 10, 11, 12, 24 1A, 3A, 6A 1B, 3B 5, 6 13, 14, 15, 16, 25 4A, 5A, 7A 4B, 6B 10, 11 7 17, 18 5A 5B, 6B 8 10, 11, 19, 20, 21, 22, 23, 25 1A, 2A, 3A, 4A, 5A, 6A, 7A, 8A 1B, 2B, 3B, 4B, 5B, 6B, 7B Describe the use and content of the statement of changes in equity. *9 A Problems 12 Study Objectives 9A 25, 26 13 23, 24, 25 3A, 8A 3B, 7B *Note: All asterisked Questions, Exercises, and Problems relate to material contained in the appendix to the chapter. Copyright © 2011 John Wiley & Sons, Inc. Weygandt, IFRS, 1/e, Solutions Manual (For Instructor Use Only) 11-1 ASSIGNMENT CHARACTERISTICS...
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...Chapter 5, Problem 1. The equivalent model of a certain op amp is shown in Fig. 5.43. Determine: (a) the input resistance. (b) the output resistance. (c) the voltage gain in dB. 8x104vd Figure 5.43 for Prob. 5.1 Chapter 5, Solution 1. (a) (b) (c) Rin = 1.5 MΩ Rout = 60 Ω A = 8x104 Therefore AdB = 20 log 8x104 = 98.0 dB Chapter 5, Problem 2 The open-loop gain of an op amp is 100,000. Calculate the output voltage when there are inputs of +10 µV on the inverting terminal and + 20 µV on the noninverting terminal. Chapter 5, Solution 2. v0 = Avd = A(v2 - v1) = 105 (20-10) x 10-6 = 1V PROPRIETARY MATERIAL. © 2007 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual, you are using it without permission. Chapter 5, Problem 3 Determine the output voltage when .20 µV is applied to the inverting terminal of an op amp and +30 µV to its noninverting terminal. Assume that the op amp has an open-loop gain of 200,000. Chapter 5, Solution 3. v0 = Avd = A(v2 - v1) = 2 x 105 (30 + 20) x 10-6 = 10V Chapter 5, Problem 4 The output voltage of an op amp is .4 V when the noninverting input is 1 mV. If the open-loop gain of the op amp is 2 × 106, what is the inverting...
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