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Operations Research

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I need help solving this problem and also I need to know exactly what the constraints are for this problem and how to figure out the constraints.

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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.

(see chart in attached file)

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.
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This is an operations research problem to determine the optimal solution for product design of cereal.

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