It is stated in the text that the development of the path of steepest ascent makes use of the assumption that the model is truly first-order in nature. However, even if there is a modest amount of curvature or interaction in the system, the use of steepest ascent can be extremely useful in determining a future experimental region. Suppose that in a system involving x1 and x2 the actual model is given by E(y) = 14 + 5x1 − 10x2 + 3x1x2 Assume that x1 and x2 are in coded form.

(a) Show a plot of the path of steepest ascent (based on actual parameters) if the interaction is ignored.

(b) Show a plot of the path of steepest ascent for the model with interaction. Note that this path is not linear.

(c) Comment on the difference in the two paths.