CPA-U QUANTITATIVE TECHNIQUES LEVEL 1 PAPER 2 STUDY TEXT

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1 CPA-U QUANTITATIVE TECHNIQUES LEVEL 1 PAPER 2 STUDY TEXT 1

2 TOPIC 1 Introduction Objectives At the end of this topic, students should be able to: i. Explain understand what quantitative techniques is all about ii. iii. iv. Describe the phases of managerial decision process Explain the components of a mathematical model for decision making Relate different quantitative models to problem solving scenario Definition of Quantitative analysis This is the process of analyzing information and making decisions using numerical data. It is also referred to in different terms: Quantitative techniques Management mathematics Operations research Business mathematics Management science Quantitative analysis assists the management of an organization in: Planning the allocation of resources at their disposal Control the use of resources in an efficient/effective way in order to achieve predetermined objective Resources at the disposal of management may include: Personnel Materials 2

3 Machinery Money Time Levels of Decisions The levels at which management decisions are made are generally categorized into three: Strategic decisions Managerial decisions Operating decisions Phases of a Managerial Decision Problem 1. Problem definition This involves: Diagnosis of the problem from its symptoms if not obvious (i.e. what is the problem?) Delineation of the sub problem to be studied. Often we have to ignore parts of the entire problem. Establishment of objectives, limitations and requirements. 2. Formulation as a mathematical model - It may be that a problem can be modeled in differing ways, and the choice of the appropriate model may be crucial to the success of the project. In addition to algorithmic considerations for solving the model (i.e. can we solve our model numerically?) we must also consider the availability and accuracy of the real-world data that is required as input to the model. 3. Model testing (or algorithm validation) 3

4 Model validation involves running the algorithm for the model on the computer in order to ensure: The input data is free from errors The model can accurately predict the effect of changes in decision variables on the objective function The results of applying the model seem reasonable (or if they are surprising we can at least understand why they are surprising). Sometimes we feed the algorithm historical input data (if it is available and is relevant) and compare the output with the historical result. 4. Solution of the model - The solution may be determined either through a manual process or the application of computer algorithm. In practice, a "solution" often involves very many solutions under varying assumptions to establish sensitivity. For example, what if we vary the input data (which will be inaccurate anyway), then how this will affect the values of the decision variables? What will be the effect of changing constraints? What of changes in the objective function? Questions of this type are commonly known as "what if" questions. 5. Implementation - This involves decision on the decision variables and constraints. In the first instance detailed instructions on what has to be done (including time schedules) to implement the results must be issued. In the second instance operating manuals and training schemes will have to be produced for the effective use of the algorithm as an operational tool. Components of a Mathematical Model in Solving Business Problems An objective function Mathematical statement of what the management wishes to achieve once the problem is solved optimally Decision variables - the unknowns to be determined by the solution to the model Constraints - the physical limitations of the system, especially applying to resources A solution (or optimal solution) - the identification of a set of the decision variable values which are feasible (i.e. satisfy all the constraints) and which lead to the optimal value of the objective function. 4

5 This is a SAMPLE (Few pages have been extracted from the complete notes:-it s meant to show you the topics covered in the full notes and as per the course outline Download more at our websites: To get the complete notes either in softcopy form or in Hardcopy (printed & Binded) form, contact us on: Call/text/whatsApp / naarocom@gmail.com info@naarocom.com sales@naarocom.com Get news and updates by liking our page on facebook and follow us on Twitter 5

6 Sample/preview is NOT FOR SALE TOPIC 2 Application of Matrix Algebra Objectives At the end of this topic, students should be able to: Apply matrices in addition subtraction and multiplication Determine the inverse of a matrix Apply matrix algebra in solving equations Apply matrix algebra in input-output analysis Apply matrix algebra in the markov process. Definition A matrix is a rectangular array of numbers of the order (size) m x n, where m is the number of rows and n is the no of columns e.g., A = 1 6 B = C = Order 3 x 2 Order 2 x 4 Order 3 x 3 The numbers in the matrix can be positive or negative, whole numbers or decimals and are referred to as elements. A matrix is denoted by a capital letter. Types of Matrices Column matrix A matrix with a single column. The order of the matrix is mx1 8 7 e.g., C = 12 of order 3 x 1 or D = 4 of order 2 x 1 9 Row matrix A matrix with a single row. The matrix is of order 1xn 6

7 E = order 1 x 3 OR F = of order 1 x 5 Square matrix - A matrix where the number of rows is equal to the number of columns i.e. m=n e.g., G = of order 3 x Null or zero matrix A matrix in which all the elements are zero H = order 2 x This is a SAMPLE (Few pages have been extracted from the complete notes:-it s meant to show you the topics covered in the full notes and as per the course outline Download more at our websites: To get the complete notes either in softcopy form or in Hardcopy (printed & Binded) form, contact us on: Call/text/whatsApp /

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ANALYTICAL CHEMISTRY 1 LECTURE NOTES

ANALYTICAL CHEMISTRY 1 LECTURE NOTES FUNDAMENTALS OF PRE ANALYSES TOPIC 1: Theory of Errors 1.0 Introduction Analytical chemistry is a specialised aspect of chemistry that deals with both qualitative analysis