Cornell (2002) describes an experiment to make a fruit punch composed of three types of juice: x1: watermellon, x2: pineapple, and x3: orange. The general acceptance of the fruit punch was to be determined by a taste panel that would rate them on a 1 to 9 scale where 1=dislike extremely, 5=neither like nor dislike, and 9=like extremely. If the proportions of the three juices are restricted by cost according to the inequalities below

(a) Graph the restricted experimental region within the simplex.

(b) Create a design appropriate for tting the Schee linear model.

(c) Create a design appropriate for tting the Schee quadratic model.

(d) Would there be any value in including an overall centroid or other interior points in the design?

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0.20 < 1 < 0.80 0.102 < 0.40 0.1030.50