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 to the effect that he could sell all the automobiles that the factory could produce by the end of the year. The factory manager was told to go ahead as fast as he wished and turn out all the cars he could up to a total of three thousand five hundred cars. The schedule line was accordingly changed from the second week in October, by drawing the line so that it came out at three thousand five hundred cars at the end of the year. It will be noticed that, though the factory had a setback due to delayed material in the second week in October, it was able to exceed the new schedule during the early part of November and it made the three thousand five hundred cars by the end of the year as requested.

The foregoing account will give a fair idea of the application of cumulative curves to problems involving output and sales. In work of this sort, the cumulative curve is one of the most valuable aids to the busy executive. The last point on the curve gives him the total output since the beginning of the period for which the curve was plotted. From the angle of the curve he can see the rate of output for any period of time he may wish to consider. It must be kept in mind that a cumulative curve never trends downward. It can move only upward or horizontally. If there is no output during any period of time the curve simply moves horizontally. Like a clock recording time, it cannot go backward.

Though the cumulative curve proper cannot go backward, a modified curve may nevertheless be made to show quantities which have been added to and subtracted from, giving total net quantities. Thus the modified cumulative curve may be used to show the quantities of stock on hand, additions to stock being plotted upward and reductions to stock being plotted downward. Any point on the curve then shows the quantities on hand at that particular time. In making a curve like this it is ordinarily the practice to strike a balance of the additions and reductions for the latest period of time, and then to change the curve only by the net amount added or taken away. Such a curve gives not only a perpetual inventory in the last point plotted, but it shows the quantity on hand at different seasons of the year as a guide for future operations. A curve of this kind can be plotted for the total number of men employed in a large organization just as well as for quantities of goods in store rooms.

Fig. 134 was photographed from a sheet of co-ordinate paper specially ruled for convenience in curve plotting. The paper is eight