(Courtesy of Noel Pollen) A food science class plans to do an experiment to compare formulations of an orange drink. There are three ingredients that can be manipulated: (1) amount of orange flavoring...

(Courtesy of Noel Pollen) A food science class plans to do an experiment to compare formulations of an orange drink. There are three ingredients that can be manipulated: (1) amount of orange flavoring (5, 15, or 25 mL); (2) amount of citric acid (5, 15, or 25 mL); and (3) amount of sucrose (200, 300, or 400 mL). The goal of the experiment is to develop an orange drink product that matches the flavor intensity of a competitor’s product. Your task is to propose two possible experimental designs for this project, each using 15 treatment combinations. For each proposed design do the following:

(a) List the treatment combinations in both coded and uncoded form. Give the name of the design.

(b) Draw a three-dimensional diagram of the treatment combinations included in the design.

(c) For the 200-mL level of sucrose, draw a contour plot of the variance of the value predicted (y) as a function of the levels of orange flavoring and citric acid. Assume that a full second-order polynomial will be fitted to the data.