4. Consider performing a response surface experiment using the paper heli-

copters described in exercise 1 of Chapter 2 and Sections 3.2 and 3.3.

(a) Create a response surface design of your choice by varying wing length between 3.5 inches and 7 inches and the width of the helicopters from 2.25 inches to 5.5 inches. Randomize your list.

(b) Construct and test your helicopters by measuring their ight time with a stopwatch.

(c) Fit the general quadratic model to your data, and test the adequacy of your model.

(d) Using canonical analysis, ridge analysis or numerical optimization, de-

termine the helicopter dimensions that you predict would result in the maximum ight time. Make a contour plot to visually verify your pre-

dicted optimum.

(e) Actually construct a helicopter of the dimensions you predict to be op-

timal. Test this helicopter by dropping it repeatedly and recording the ight time. Are the ight times comparable to your predictions?