Quantitative Analysis for Management, 13/e

M6.4 Maximum and Minimum

In using quantitative techniques in business, we often try to maximize profit or minimize cost. If a profit function or cost function can be developed, taking a derivative may help us to find the optimum solution. In dealing with nonlinear functions, we often look at local optimums, which represent the maximums or minimums within a small range of X.

Figure M6.4 illustrates a curve where point A is a local maximum (it is higher than the points around it), and point B is a local minimum (it is lower than the points around it); however, there is no global maximum or minimum, as the curve continues to increase without bound as X increases, and to decrease without bound as X decreases. If we place limits on the maximum and ...