You've already done your experiment, and it was very expensive. Unfortunately, you did not find the answer you were looking for even though all of your experience and intuition tell you that the answer is buried in the data somewhere. Every day, experiments are abandoned as failures when the real failure is in the analysis of the experiment. The right answer is often there, but it is invisible without the right tools. We can do better.
Contour plots are simple and effective for two-factor experiments.
Add a third factor and finding the sweet spot becomes tricky. Add a fourth, and you quickly get to feel like you are looking for a needle in a haystack. Mountain-climbing algorithms were utilized to overcome the weaknesses of visual inspection. This approach was very popular in the eighties because it runs very fast even on slow computers. Unfortunately, mountain-climbing does not always find the best answer even when combined with sophisticated random seeding strategies.