Burnside Marketing Research conducted a study for Baker Foods on some designs 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. Wheat/ Corn Sweetener Flavor Bits Child Low High Sugar Honey Artificial Present Absent 1 15 35 30 40 25 15 9 2 30 20 40 35 35 8 11 3 40 25 20 40 10 7 14 4 35 30 25 20 30 15 18 5 25 40 40 20 35 18 14 6 20 25 20 35 30 9 16 7 30 15 25 40 40 20 11 a. Suppose the overall utility (sum of part-worths) of the current favorite cereal is 75 for each child. Formulate a linear programming model that can be used to determine the product design that will maximize the share of choices for the seven children in the sample. Determine the optimal solution. b. Assume the overall utility of the current favorite cereal for children 1-4 is 70, and the overall utility of the current favorite cereal for children 5-7 is 80. Modify the linear programming model used to determine the product design that will maximize the share of choices for the seven children in the sample. Determine the new optimal solution.