Our experimenter begins by fixing temperature and varying time. The yield rises from 30% to over 40%, but soon begins to drop off again. Time is fixed at its best level and now temperature is varied. This affects the yield in a similar way and the best temperature is chosen. At this point, the experimenter concludes that the optimum has been found.
With the contour map to look at, it is easy to see what went wrong. Increasing time would have had a much greater impact on yield at a lower temperature. In other words, the key to understanding the system lies in the interaction between the two factors.