The USDA is responsible for managing and administrating the
The USDA is responsible for managing and administrating the
The USDA is responsible for managing and administrating 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 issue do USDA must consider how much it cost to obtain a nutritional well-balanced diet for men and women in various age groups. As a first step in the process the USDA identified and analyzed 31 different food groups and determine the contributions a serving from each group makes 24 different nutritional categories. A partial listing of this information is given below. Food Weekly Units Kilo-calories Protein Vitamin A Thiamin Ribo-flavin Niacin Vitamin B6 Vitamin B12 Folacin Vitamin C Vitamin E Calcium Iron Magne-sium Phos-phorous Zinc Sodium Carbo-hydrates Total Fat Saturated Fat Monosat. Fats Polysat. Fat Choles- terol Sugar Cost per unit Pref. Rating Potatoes 0 4.29 10.40 0.06 0.43 0.16 7.20 1.22 0.00 50.00 74.00 0.34 0.39 3.4 103 2.38 1.7 1.18 93.80 2.60 1.10 0.80 0.40 2.00 0.00 $0.391 6.68 High-Nutrient Vegetables 0 1.39 5.90 192.86 0.22 0.25 2.60 0.47 0.00 123.00 108.00 5.08 1.57 3 72 1.2 1.1 4.31 30.80 1.00 0.10 0.10 0.40 0.00 4.00 $1.014 17.81 Other Vegetables 0 1.81 8.10 18.35 0.22 0.22 2.50 0.30 0.03 125.00 27.00 1.20 0.84 3 66 1.61 1.6 8.41 37.10 2.00 0.40 0.50 0.80 0.00 16.00 $0.958 13.31 Mixtures; mostly vegetable 0 16.42 21.80 11.49 0.46 0.26 12.10 1.80 0.03 197.00 108.00 16.34 1.27 5.6 201 5.05 3.2 35.10 174.40 101.00 26.10 21.10 10.80 0.00 256.00 $1.897 24.5 Vitamin-C-rich fruits 0 3.41 5.00 7.33 0.56 0.16 1.70 0.30 0.30 242.00 280.00 0.76 0.85 1.1 74 1.07 0.4 0.09 81.90 0.70 0.00 0.10 0.10 0.00 4.00 $0.721 15.9 Other fruit 0 2.81 1.90 3.64 0.10 0.15 1.10 0.60 0.00 25.00 24.00 1.76 0.30 1.1 42 0.47 0.3 0.08 71.40 1.60 0.30 0.30 0.40 0.00 32.00 $0.961 14.88 Whole-grain/high-fiber breakfast cereals 0 16.73 63.40 135.09 5.98 5.62 67.20 6.23 15.40 896.00 134.00 38.10 8.19 82.2 657 20.45 18.6 19.89 323.60 21.90 4.60 6.90 8.90 0.00 140.00 $2.770 8.22 Other cereals 0 17.44 34.90 143.65 5.46 5.77 72.80 7.09 7.24 1280.00 168.00 5.60 1.76 57.2 127 4.83 12.6 32.54 382.30 6.20 2.50 1.10 1.80 0.00 392.00 $3.327 9.43 Whole-grain/high-fiber flour, meal, rice 0 16.19 47.70 2.55 1.40 0.56 10.50 1.33 0.00 102.00 0.00 2.89 5.39 11.4 595 18.05 11.5 22.68 328.50 17.90 2.70 4.30 8.80 0.00 8.00 $0.966 4.4 Other flour, meal, rice, pasta 0 16.44 42.10 0.60 20.50 1.19 18.00 0.54 0.01 59.00 0.00 1.26 6.53 17.1 141 11.12 4.3 17.47 346.00 6.20 1.20 2.30 11.00 52.00 52.00 $0.720 0.28 Whole grain/high fiber bread 0 11.18 35.60 1.16 1.45 1.03 14.30 8.26 0.00 177.00 0.00 1.33 3.64 12.2 284 8.37 5.6 20.12 217.10 14.90 2.60 3.70 6.40 1.00 4.00 $1.553 5.52 Other breads 0 12.28 35.90 0.48 1.99 1.46 17.00 0.24 0.02 151.00 0.00 1.53 4.92 13.1 109 5.61 2.8 25.28 225.10 18.60 4.30 7.10 5.20 7.00 16.00 $1.111 4.9 Bakery products 0 19.54 34.10 4.66 1.45 1.25 14.10 0.27 0.46 85.00 1.00 7.21 2.61 14.6 108 5.65 2.8 31.36 300.40 69.10 21.50 27.20 14.30 112.00 392.00 $2.460 9.03 Grain mixtures 0 12.23 49.60 13.07 1.25 1.00 11.30 0.48 0.84 54.00 7.00 1.48 5.53 8 107 6.99 4.8 38.73 196.80 25.10 9.50 8.60 4.80 61.00 24.00 $1.556 25.67 Milk, yogurt 0 3.42 20.30 9.53 0.23 1.00 0.71 0.24 2.10 31.00 6.00 0.65 7.27 0.4 79 5.77 2.5 3.26 32.00 14.80 9.30 4.10 0.60 60.00 4.00 $0.362 17.34 Cheese 0 16.73 105.60 46.66 0.12 1.64 0.42 0.33 3.30 55.00 0.00 3.60 30.51 2.3 117 27.29 13.4 43.54 10.50 134.40 85.15 38.30 4.00 413.00 0.00 $2.811 22.72 Cream, mixtures mostly milk 0 10.16 16.20 17.48 0.18 1.00 0.59 0.19 1.91 14.00 3.00 1.31 5.70 0.76 66 4.61 4 4.34 107.30 60.50 41.80 13.50 2.00 137.00 256.00 $1.223 17.1 Lower-cost red meats, variety meats 0 10.87 73.90 52.08 0.39 1.25 15.00 0.77 17.35 92.00 7.00 1.02 0.38 8.6 65 6.12 15.5 5.18 1.30 84.90 33.60 37.10 4.50 284.00 0.00 $1.918 44.58 Higher-cost red meats, variety meats 0 9.45 72.10 0.07 0.92 0.75 14.10 0.90 6.03 18.00 7.00 0.89 0.29 5.6 67 6.8 10.9 6.90 0.60 74.00 28.30 32.50 5.90 278.00 0.00 $2.801 89.24 Poultry 0 6.43 61.10 13.26 0.14 0.52 16.20 0.80 2.15 45.00 5.00 1.18 0.41 4 52 4.18 5.3 2.05 0.40 42.10 12.00 16.90 9.20 271.00 0.00 $1.281 57.53 Fish, shellfish 0 4.01 65.00 2.53 0.20 0.36 14.80 0.69 9.69 28.00 2.00 2.71 1.85 3.8 111 7.67 5.9 8.17 2.40 12.70 2.70 4.30 3.80 172.00 4.00 $3.471 78.18 Bacon, sausage, luncheon meats 0 17.92 53.20 8.69 1.13 0.72 12.50 0.75 6.39 16.00 69.00 1.35 0.64 5.2 47 5.07 7.8 41.64 7.60 170.40 63.00 79.10 18.40 287.00 16.00 $2.481 17.83 Eggs 0 5.97 50.00 25.50 0.20 1.93 0.30 0.53 3.31 141.00 0.00 3.62 1.96 5.7 40 7.11 4.4 5.04 4.90 40.10 12.40 15.24 5.50 1698.00 0.00 $0.838 9.35 Dry beans, peas, lentils 0 12.84 82.60 1.52 0.93 0.64 3.80 0.82 0.00 548.00 11.00 1.68 4.06 19.7 452 12.86 9.35 4.72 235.60 5.00 1.30 1.00 1.80 5.00 44.00 $1.309 13.08 Mixtures, mostly meat, poultry, fish, egg 0 7.20 37.10 55.65 0.50 0.53 10.10 0.53 1.76 50.00 15.00 3.77 1.19 5.4 73 6.97 4.7 29.10 58.40 37.70 11.70 14.70 8.00 101.00 20.00 $1.967 46.2 Nuts, peanut butter 0 25.71 102.50 0.71 1.16 0.48 50.30 1.61 0.00 402.00 1.00 36.76 2.14 9.3 726 15.28 13.5 16.74 88.60 221.70 37.80 102.00 71.10 0.00 56.00 $2.504 21.26 Fats, oils 0 33.41 2.50 74.98 0.02 0.07 0.00 0.23 0.38 9.00 0.00 54.49 0.66 0.4 6 0.65 0.2 23.59 14.80 370.00 90.40 137.20 125.80 152.00 24.00 $1.198 3.17 Sugar, sweets 0 16.46 3.50 0.48 0.05 0.11 1.00 0.04 0.11 7.00 1.00 0.47 0.75 2.5 33 0.88 0.56 1.78 406.90 7.30 4.00 2.33 0.50 3.00 1576.00 $1.111 2.39 Seasonings 0 1.89 8.00 38.79 0.14 0.24 2.17 0.52 0.00 63.00 21.00 0.58 6.33 51.1 1780 2.23 2.5 941.11 36.30 5.50 1.80 1.70 1.20 0.00 4.00 $2.077 5.8 Soft drinks, punches, ades 0 2.31 0.20 12.49 0.02 0.01 0.00 0.00 0.00 97.00 108.00 0.00 0.54 0.4 5 0.6 0.2 0.59 58.40 0.00 0.00 0.00 0.00 0.00 116.00 $0.249 47.42 Coffee, tea 0 4.68 20.00 0.00 0.02 0.79 44.50 0.10 0.00 254.00 0.00 0.01 2.74 10.2 778 4.79 1.7 1.13 87.70 1.70 0.60 0.10 0.50 0.00 4.00 $6.018 7.7 Weekly Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 $0.000 0 Weekly Lower Limit 203.00 434.00 350.00 10.50 11.90 133.00 14.00 14.00 1400.00 420.00 70.00 61.95 70 2450 61.95 105.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weekly Upper Limit 203.00 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 9999 324.80 9999 676.67 225.56 9999 9999 2100 2436
The last two rows in the spreadsheet indicate the minimum and or maximum nutrients required per week for men between the ages of 20 and 50. (maximum values of 9999 indicate that new maximum value applies to that particular nutritional requirement)
The USDA uses this information to design a diet that meets the indicated nutritional requirements. The last two columns in the figure above represents the 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 unsatisfactory to the tastes of the people who are expected to eat it. To help address this issue the USDA conducted a survey to assess people’s preferences for different food groups. The last column in the figure above summarizes these preference ratings with higher scores indicating more desirable foods and lower scores indicating less desirable foods. Thus another objective that could be pursued is determining the diet that meets the nutritional requirements and produces the highest total preference rating.
However this solution is likely to be quite expensive. Assume that the USDA has asked you to help them analyze the situation using MOLP.
Find the weekly diet that meets the nutritional requirements in the least costly matter. What is the lowest possible minimum cost? what preference rating does the solution have?
Find the weekly diet that meets the nutritional requirements with the highest preference rating. What preference rating does this solution have? What cost is associated with this solution?
Find the solution that minimizes the maximum percentage deviation from the optimum values for each individual objectives. What cost and preference rating is associated with this solution?
Suppose the deviations from the optimal calls value our way to twice as heavily as theirs from the optimal preference value. Find a solution that minimizes the maximum weighed percentage deviations. What cost and preference rating is associated with this solution?
What other factors were constraints why you want to include in this analysis if you had to eat the resulting diet?
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