TAILIEUCHUNG - Quantitative Methods for Business chapter 3

C H A P T E R 3 Dealing with curves without going round the bend Chapter objectives This chapter will help you to: ■ ■ ■ ■ deal with types of non-linear equations interpret and analyse non-linear business models apply differential calculus to non-linear business models use the Economic Order Quantity (EOQ) model for stock control ■ become acquainted with business uses of EOQ model In the last chapter we looked at how linear equations, | CHAPTER 3 Dealing with curves without going round the bend Chapter objectives This chapter will help you to deal with types of non-linear equations interpret and analyse non-linear business models apply differential calculus to non-linear business models use the Economic Order Quantity EOQ model for stock control become acquainted with business uses of EOQ model In the last chapter we looked at how linear equations equations that represent straight lines can be used to model business situations and solve business problems. Although important their limitation is that the relationships they are used to model need to be linear for them to be appropriate. There are circumstances when this is not the case for instance the sort of model economists use to represent the connection between volume of production and cost per unit. In such a model economies of scale mean that the average cost of production per unit gets lower as output increases. The equation representing the situation would be non-linear and we might be interested in analysing it to find the least cost level of output. 82 Quantitative methods for business Chapter 3 In this chapter we will look at the features of basic non-linear equations and use them to analyse business operations. Following this we will consider how to find optimal points in non-linear business models using simple calculus. Later in the chapter you will meet the Economic Order Quantity model a non-linear business model that organizations can use in determining their best stock ordering policy. Simple forms of non-linear equations One thing you might have noticed about the linear equations that featured in Chapter 2 was the absence of powers. We met terms like 60Q and but not 3Q2 or 3 x. The presence of powers or for that matter other non-linear forms like sines and cosines although we will not be concerned with them here distinguishes a non-linear equation. In order to appreciate why consider two possible relationships between x .

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