Burnside Marketing Research conducted a study for Barker Foods on several formulations for a new dry cereal. Three attributes were found to be most influential in determining which cereal had the best taste: ratio of wheat to corn in the cereal flake, type of sweetener (sugar, honey, or artificial), and the presence or absence of flavor bits. Seven children participated in taste tests and provided the following part-worths for the attributes (see Section 13.4 for a discussion of part-worths):

a. Suppose that the overall utility (sum of part-worths) of the current favorite cereal is 75 for each child. What product design will maximize the number of children in the sample who prefer the new dry cereal? Note that a child will prefer the new dry cereal only if its overall utility is at least 1 part-worth larger than the utility of their current preferred cereal.

b. Assume that the overall utility of the current favorite cereal for children 1 to 4 is 70, and the overall utility of the current favorite cereal for children 5 to 7 is 80. What product design will maximize the number of children in the sample who prefer the new dry cereal? Note that a child will prefer the new dry cereal only if its overall utility is at least 1 part-worth larger than the utility of their current preferred cereal.