The United States Department of Agriculture (USDA) is responsible for managing and administering the national food stamp program. This program provides vouchers to low-income families that can be used in place of cash to purchase food at grocery stores. In determining the cash value of the vouchers issued, the USDA must consider how much it costs to obtain a nutritional, well-balanced diet for men and women in various age groups. As a first step in this process, the USDA identified and analyzed 31 different food groups and determined the contributions a serving from each group makes to 24 different nutritional categories.

The USDA uses this information to design a diet that meets the indicated nutritional requirements. The last two columns of the Xcel file represent two different objectives that can be pursued in creating a diet. First, we may want to identify the diet that meets the nutritional requirements at a minimum cost. Although such a diet might be very economical, it might also be very unsatisfactory to the tastes of the people who are expected to eat it. To help address this issues, the USADA conducted a survey to assess people’s preferences for different food groups. The last column in Xcel file 7.19 summarizes these preferences ratings, with the higher scores indicating more desirable foods, and lower scored indicating less desirable foods. Thus, another objective that could be pursued would be that of determining the diet that meets the nutritional requirements and produces the highest total preference rating. However, the solution is likely to be quite expensive. Assume that the UDSA has asked you to help them analyze this situation using MOLP.

Answer the following questions:

1. Find the weekly diet that meets the nutritional requirements in the least costly manner. What is the lowest possible minimum cost? What preference rating does this solution have?

2. Find the weekly diet that meets the nutritional requirements with the highest preference rating. What preference rating dies this solution have? What cost is associated with this solution?

3. Find the solution that that minimizes the maximum percentage deviation from the optimum values for each individual objective. What cost and preference rating is associated with this solution?

4. Suppose that deviations from the optimal cost value are weighted twice as heavily as those from the optimal preference value. Find the solution that minimizes the maximum weighted percentage deviations. What cost and preference rating is associated with this solution.

5. What other factors or constraints might you want to include in this analysis if you had to wat the resulting diet?