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Quantitative Methods for Business chapter 2

C H A P T E R 2 Getting linear models straight Chapter objectives This chapter will help you to: ■ ■ ■ ■ ■ ■ plot and solve linear equations apply basic break-even analysis interpret inequalities undertake simple linear programming using graphs use the technology: Solver in EXCEL become acquainted with business uses of linear programming | CHAPTER 2 Getting linear models straight Chapter objectives This chapter will help you to plot and solve linear equations apply basic break-even analysis interpret inequalities undertake simple linear programming using graphs use the technology Solver in EXCEL become acquainted with business uses of linear programming This chapter is intended to introduce you to the use of algebra in solving business problems. For some people the very word algebra conjures up impressions of abstract and impenetrable jumbles of letters and numbers that are the preserve of mathematical boffins. Certainly parts of the subject of algebra are complex but our concern here is with algebraic techniques that help to represent or model business situations. In doing this we are following in the footsteps of the father of algebra Mohammed ibn-Musa al-Khwarizmi. In the ninth century al-Khwarizmi wrote Al-jabrwa l-muqabala which might be translated as Calculation Using Balancing and Completion . The first part of the Arabic title gives us the word algebra. Although al-Khwarizmi was a scholar working at the House of Wisdom in Baghdad he saw his task in very practical terms namely to focus on . what is easiest and most useful in arithmetic such as men constantly require in cases of inheritance legacies partitions law-suits and trade Chapter 2 Getting linear models straight 33 and in all their dealings with one another. cited in Boyer 1968 p. 252 In the course of this chapter we will confine our attention to simple algebra and how you can use it to solve certain types of business problem. We will focus on linear equations which are those that are straight lines when they are plotted graphically. They form the basis of linear models that assist business problem-solving. 2.1 Linear equations Central to algebra is the use of letters most frequently x and y to represent numbers. Doing this allows us to deal systematically with quantities that are unknown yet of importance in an analysis. These unknown