Quantitative Analysis for Management, 13/e

M6.5 Applications

There are many problems in which derivatives are used in business. We discuss a few of these here.

Economic Order Quantity

In Chapter 6, we show the formula for computing the economic order quantity (EOQ), which minimizes cost when certain conditions are met. The total cost formula under these conditions is

The EOQ model is derived from the total inventory cost function.

$$\begin{array}{c}\text{Total cost = (Total ordering cost) + (Total holding cost) + (Total purchase cost)}\\ TC=\frac{D}{Q}{C}_0+\frac{Q}{2}{C}_h+DC\end{array}$$

where

$$\begin{array}{l}Q=orderquantity\hfill \\ D=annualdemand\hfill \\ C_o=orderingcostperorder\hfill \\ C_h=holdingcostperunitperyear\hfill \\ C=purchase(material)costperunit\hfill \end{array}$$

The variable is Q, and all of the others are known constants. The derivative of the total cost with respect to