FOUNDATION REVIEW
Contents
FR.1 Graphing linear inequalities 2
FR.2 The linear programming model 7
FR.3 Interpreting linear programming results 13
Review questions 16
Introduction
Linear programming is commonly used in short-term operations planning. In MA2, you will use linear programming and its related concepts to make relevant management accounting decisions. Knowing how to formulate and interpret a linear program will help you determine the optimum production plan to analyze various overhead costing schemes, to decide whether to make or buy a product, and to solve special order problems. These problems will factor in capacity cost. These concepts will be referenced in Lessons 3 and 10. Formulation is the most critical component in understanding linear programming. This is the process that transforms a cost or management accounting problem into a format computer algorithms can solve within fractions of a second. It is the interpretation of the results that is important. In Lesson 3, you will learn to use a tool in Excel called Solver to solve linear programming problems. The purpose of this Foundation Review is to review the concepts related to linear programming. You will not be asked to solve problems graphically in MA2; however, you will be asked to formulate linear programming models, solve problems, and interpret your results using Solver. The graphing technique is illustrated so that you can review the concepts of linear programming using simple examples.
Note:
This Foundation Review is optional; there is no assignment to submit. If you know this material well, just skim through it and proceed with the course. You can assess your strengths and weaknesses with the Review Questions and Solutions provided at the end of this review. Try the problems without referring to the solutions until you are finished. If you need further practise in a particular area, refer to Lesson 10 of Quantitative Methods [QU1]. In addition, you can reference Mathematics for Business: The CGA Reference Handbook, pages 72-97.
Overview
Linear programming is a mathematical technique that was developed to help managers make better decisions. It is called linear programming because it involves solving sets of simultaneous linear equations. The technique has applications in many diverse areas. For example, a manufacturer might be interested in designing a production schedule that minimizes total production, inventory holding, and labour change-over costs. A financial analyst might want to find the best portfolio for an investor. A marketing manager would like to know the best way to allocate a fixed advertising budget among different advertising media. An accounting firm might want to assign its CGAs to different clients in order to minimize the total time needed to complete a set of jobs. All these problems can be handled by linear programming. The common theme to each problem is that one wants to minimize or maximize some quantity (usually cost or profit), which is the objective, within certain resource restrictions, which are called constraints. In general, there are three types of constraints:
• resource constraints, which determine the available resources such as labour hours, machine hours, and raw materials
• structural constraints, which describe the production and use of products
• marketing constraints, which indicate the maximum or minimum sales levels of products This review demonstrates how such problems are mathematically formulated as linear programs. It discusses what is known as the graphical simplex method to solve simple linear programs, and the sensitivity (what-if) analysis with respect to different problem parameters.
Learning objectives
• Identify the slope and the yintercept in the equation for a straight line.
• Graph an equation for a straight line.
• Determine the point of intersection of two lines algebraically and graphically.
• Graph linear inequalities.
• Set up a problem as