...DESCRIPTION: This course is designed for Commerce and Accountancy students which deals with the basic algebraic expressions, linear equations and inequalities, solving problems in a linear programming involving graphical method, simplex method, transportation method and assignment method, the break even analysis, the decision theory, business forecasting and inventory. GRADING SYSTEM: To obtain a passing mark, students should at least master 75% of the lesson. Computations of grades are shown below: For Prelim, Midterm and Final: |Class Standing (70%) |Examination (30%) | |Quizzes (20%) |Assignment (10%) |Project(20%) |Participation(20%) | | |Tentative Grade = Class standing + Examination | |Final Grade = Prelim (30%) + Midterm (30%) + Final (40%) | COURSE CONTENT: |Time Allotment |Unit Content |Specific Objectives |Teaching Methods |Activities / Projects / |Mode of Assessment | | |...
Words: 1015 - Pages: 5
...A look at linear programming, using the simplex method Earlier in the class we were introduced to linear programming and now we are going to introduce a different method using a more geometric version called the simplex method. First, I am going to have to explain theory of the simplex method and then we’ll explain the real world uses of this algebraic math Ok, so earlier in the class we were introduced into liner equations and inequalities. With the simplex method we are going got look for what is called “The Optimum Solution”, but in order to find the optimum solution we need to change the linear equation so that it can be recognized differently and computer in geometric form as well as on our graph. We are now going to use a special matrix or TABLEAU to find the many variables and to solve for an optimum solution by substituting some of our variables into our sometimes large programming problem. I must say that the problem could sometimes result in a solution or it may also have no solution at all. Once we find that some of the test are confirmed with the simplex method and we come to the optimal solution the process itself stops. With this method we don’t have to consider that the amount of corner point will increase with the amount of variables, since we are only looking for the optimal solution. In the text we are given many examples of what this simplex method of linear programming problems. As I have read throughout the chapters I see that the most probable applications...
Words: 406 - Pages: 2
...BASIC LINEAR PROGRAMMING 18.0 LEARNING OBJECTIVES After studying this chapter, readers should be able to: Understand the concept and meaning of linear programming; Know the underlying basic assumptions; Formulate the linear programming problem; Solve linear programming problem using graphical and Simplex methods; and make appropriate and correct interpretations; and Understand the concepts of duality and shadow cost in linear programming. 18.1 INTRODUCTION This is an Operations Research technique that is popular and frequently used in industry, business and other areas of human endeavour. The major focus of Linear Programming (L.P) technique, in decisionmaking, is to optimize the use of limited available resources. That is, it is an economic allocation of scarce resources by means of mathematical modeling. The history of Operations Research tells us that George B. Dantzing developed Linear Programming technique during Second World War. His primary aim of developing the technique then was to solve some military logistics problems. But now, it is being used extensively in wide areas of human endeavours. 18.2 CONCEPT AND MEANING OF LINEAR PROGRAMMING. The term “Linear Programming” consists of two words Linear and Programming. The word “Linear” implies linear relationship among the variables in a model while the word “Programming” implies modeling and solving a problem mathematically. By the combination of these two words, it is obvious that the Linear Programming technique...
Words: 8318 - Pages: 34
...0.1 0.1.1 Linear Programming Objectives By the end of this unit you will be able to: • formulate 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...
Words: 10505 - Pages: 43
...computer-based, visual or verbal representations are used. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes scheduling airlines, both planes and crew, deciding the appropriate place to site new facilities such as a warehouse or factory, managing the flow of water from reservoirs, identifying possible future development paths for parts of the telecommunications industry, establishing the information needs and appropriate systems to supply them within the health service, and identifying and understanding the strategies adopted by companies for their information systems. Scientific Planning Successful management relies on careful coordination, often using scientific methods in project planning. For example, critical path analysis allows us to identify which tasks in a project will take the longest or adversely affect the length of other tasks, permitting us to focus on those tasks. Computer models can also help we determine utilization and recommend more effective usage. In addition, this type analysis allows us to develop proactive strategies for handling outages and...
Words: 3150 - Pages: 13
...LINEAR PROGRAMMING II 1 Linear Programming II: Minimization © 2006 Samuel L. Baker Assignment 11 is on page 16. Introduction A minimization problem minimizes the value of the objective function rather than maximizing it. Minimization problems generally involve finding the least-cost way to meet a set of requirements. Classic example -- feeding farm animals. Animals need: 14 units of nutrient A, 12 units of nutrient B, and 18 units of nutrient C. Learning Objective 1: Recognize problems that linear programming can handle. Linear programming lets you optimize an objective function subject to some constraints. The objective function and constraints are all linear. Two feed grains are available, X and Y. A bag of X has 2 units of A, 1 unit of B, and 1 unit of C. A bag of Y has 1 unit of A, 1 unit of B, and 3 units of C. A bag of X costs $2. A bag of Y costs $4. Minimize the cost of meeting the nutrient requirements. To solve, express the problem in equation form: Cost = 2X + 4Y objective function to be minimized Constraints: 2X + 1Y $ 14 nutrient A requirement 1X + 1Y $ 12 nutrient B requirement 1X + 3Y $ 18 nutrient C requirement 8 8 Read vertically to see how much of each nutrient is in each grain. X $ 0, Y $ 0 non-negativity Learning objective 2: Know the elements of a linear programming problem -- what you need to calculate a solution. The elements are (1) an objective function that shows the cost or profit depending on what choices you make, (2) constraint inequalities...
Words: 4295 - Pages: 18
...PRICING MANAGEMENT 1. The pricing strategy used to set prices of the products that are must be used with the main product is called a) captive product pricing b) product line pricing c) competitive pricing d) optional product pricing 2. The pricing strategy in which prices are set lower to actual price to trigger short term sales is classified as a) promotional pricing b) short term pricing c) quick pricing d) cyclical pricing 3. The kind of reduction made to those buyers who buy large volumes of products is classified as a) cash discount b) seasonal discount c) functional discount d) quantity discount 4. The pricing strategy in which company divides location into different sectors and charge same price for each sector is classified as a) freight on board origin pricing b) zone pricing c) basing point pricing d) uniform delivered pricing 5. The kind of pricing strategy which allow sellers to continuously adjust prices according to needs and characteristics of customers is classified as a) fake pricing b) termed pricing c) dynamic pricing d) international pricing 6. These are all pricing objectives except: a) Survival b) Maximize profit c) Reduct possible costs and product expenses d) Product-quality leadership 7. This determines the changes in demand with unit change in price a) Price sensitivity b) Price elasticity c) Price concept ...
Words: 1116 - Pages: 5
...Operations Research and its Prospects in Pakistan Prof. Dr. Shoaib ud Din Mathematics Department Punjab University, Lahore, Pakistan Operations Research has had an increasingly great impact on the management of organizations in the recent years. In fact, with the exception of advent of electronic computer, the extent of this impact seems to be unrivalled by that of any other recent development. However, all the development in this field has gone almost unnoticed in most developing countries including Pakistan. This article is an effort to introduce Mathematics community in the country to the subject and its achievements. A brief history In order to appreciate the importance of OR in the world today it is important that we know something of its history and evolution. Although roots of Operations Research can be traced back many decades, it is generally agreed that this discipline began during World War II. During the War team of British scientists with diverse background were called upon to study the strategic and tactical problems associated with air and land defense of the country. The establishment of this scientific team marked the first formal Operations Research activity. Their efforts were allegedly instrumental in winning the Air Battle of Britain, The Island Campaign in the Pacific, the Battle of the North Atlantic, and so on. The name Operations Research-Operational Research in the United Kingdom – was apparently coined because the problems assigned to this team...
Words: 1347 - Pages: 6
...ASSIGNMENT ON OPERATION RESEARCH ( FIN – 3104 ) 3RD YEAR , 1ST SEMESTER BBA – 3RD BATCH DEPARTMENT OF FINANCE JAGANNATH UNIVERSITY TOPIC Quantitative Analysis for Optimization : Using Linear Programming & Transportation Problem Group Name Name & ID No. of the Group Members: |Sl. No. |Name |ID No. | | | | | |01 |Suman Chandra Mandal (Group Leader) |091557 | | |Md. Nahid Islam |091604 | |02 | | | | | | | |03 |Mahbuba Mehreen |091619 ...
Words: 1940 - Pages: 8
...MANAGEMENT | Core ☐ Elective x☐x | Title | Quantitative Methods II | Abbreviation | QM-II | Course Coordinator | Prof. RAVI SHANKAR | Teaching Members | | Course Revision Record Version | Version Date | Recommendation | 1 | 05 Sept 2015 | | Credits | 3 | Contact Hours | 30 | Learning Hours | 60 | Office Hours | 30 | Contact Details | 09811033937 | Course eMail | r.s.reaches@gmail.com | Course Descriptor Course Overview(200 words) | Quantitative Methods-II, focuses on ‘Operations Research’ tools which helps in solving problems in different functional domain of business. It also helps to optimize business operations/processes. The Quantitative Method-II tools act as aids to decision makers to take best decision for effective & efficient use of resources which ultimately lead to profit maximization or to achieve multiple goals or objective. | Course must be aligned with a strategic objective of the program Prerequisites/Co-requisites | Quantitative Methods I | Learning Objectives | To learn basic optimization techniques and their managerial applications with a focus on methodologies such as Linear Programming, Transportation models, Assignment Models, Transhipment Models, Games Theory, Queuing Models, Goal Programming, Integer Programming, Non-linear Programming, Simulation and Decision Theory. | Learning objectives must be aligned with learning outcomes of the course Teaching Methods | Modeling, Case study, Software-based solutions | Refer...
Words: 1342 - Pages: 6
...ons/ Points Awarded 100.00 Points Missed 0.00 Percentage 100% Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. 1. A) one and only one solution 1. B) one and only one solution 1. C) one and only one solution 1. D) infinitely many solutions 1. E) no solution Points Earned: 4.0/4.0 Solve the linear system of equations 1. A) Unique solution: 1. B) Unique solution: 1. C) Infinitely many solutions: 1. D) No solution Points Earned: 4.0/4.0 Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is the accumulated amount? 540. A) The simple interest is $140, the accumulated amount is $540. B) The simple interest is $115, the accumulated amount is $515. C) The simple interest is $120, the accumulated amount is $520. D) The simple interest is $125, the accumulated amount is $555. Points Earned: 4.0/4.0 Find the present value of $40,000 due in 4 years at the given rate of interest 8%/year compounded monthly. 948. A) The present value is $28,948.67. B) The present value is $29,433.94. C) The present value is $29,076.82. D) The present value is $29,748.06. Points Earned: 4.0/4.0 Solve the system of linear equations using the Gauss-Jordan elimination method. 1. A) B) C) D) E) Points Earned: 4.0/4.0 The following breakdown of a total of 18,686...
Words: 9617 - Pages: 39
...www.VLCglobal.com/support VLC Course Descriptions Quantitative Analysis for Decision Making Quantitative Analysis for Decision Making An Immersive Virtual Reality Learning Experience 2011-2012 Course Description This course provides the student with the concepts, methods and tools for the application of logical and quantitative analysis to business decision making and problem solving. It familiarizes the student with a wide range of software and other classical and contemporary resources related to decision and problem analysis, including basics of logic and decision making, principles of optimization, probabilistic distributions, linear programming, simplex, queuing and transportation problems, break even analysis, inventory management, forecasting and simulation. The course highlights the benefits as well as the limits of quantitative analysis in a real-world context. This course may be adapted for the graduate and undergraduate levels. Materials Readings, assignments, problems and assessments are integrated into the courseware. Any additional materials will be assigned by the instructor at the start or during the course. Course Outline & Assignments Assignments will change from time to time as new resources become available, contemporary events have bearing on the topics, or the social, legal, or economic environments change. FUNDAMENTALS OF DECISION MAKING AND PROBLEM SOLVING (Module One, 4-6 hours) • • • • • • • • • • • • • • ...
Words: 1075 - Pages: 5
...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...
Words: 30976 - Pages: 124
...Chapter 7 Linear Programming: Maximization Models © 2008 Prentice-Hall, Inc. Introduction Many management decisions involve trying to make the most effective use of limited resources Machinery, labor, money, time, warehouse space, raw materials Linear programming (LP) is a widely used mathematical modeling technique designed to help managers in planning and decision making relative to resource allocation Belongs to the broader field of mathematical programming In this sense, programming refers to modeling and solving a problem mathematically © 2009 Prentice-Hall, Inc. 7–2 Requirements of a Linear Programming Problem LP has been applied in many areas over the past 50 years All LP problems have 4 properties in common 1. All problems seek to maximize or minimize some quantity (the objective function) 2. The presence of restrictions or constraints that limit the degree to which we can pursue our objective 3. There must be alternative courses of action to choose from 4. The objective and constraints in problems must be expressed in terms of linear equations or inequalities © 2009 Prentice-Hall, Inc. 7–3 LP Properties and Assumptions PROPERTIES OF LINEAR PROGRAMS 1. One objective function 2. One or more constraints 3. Alternative courses of action 4. Objective function and constraints are linear ASSUMPTIONS OF LP 1. Certainty 2. Proportionality 3. Additivity 4. Divisibility 5. Nonnegative variables Table 1 © 2009 Prentice-Hall, Inc. 7–4 Basic Assumptions...
Words: 6763 - Pages: 28
...1 Mathematical Programming The Mathematical Programming Add-in constructs models that can be solved using the Solver Add-in or one of the solution add-ins provided in the collection. When 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...
Words: 12583 - Pages: 51
