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The last two rows in this spreadsheet indicate the minimum and/or maximum nutri- ents required per week for men between the ages of 20 and 50. (Maximum values of 9999 indicate that no maximum value

The last two rows in this spreadsheet indicate the minimum and/or maximum nutri- ents required per week for men between the ages of 20 and 50. (Maximum values of 9999 indicate that no maximum value applies to that particular nutritional requirement.) The USDA uses this information to design a diet (or weekly consumption plan) that meets the indicated nutritional requirements. The last two columns in Figure 7.20 rep- resent 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 issue, the USDA conducted a survey to assess people's preferences for different food groups. The last column in Figure 7.20 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 would be that of 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 this situation using MOLP. a. Find the weekly diet that meets the nutritional requirements in the least costly man- ner. What is the lowest possible minimum cost? What preference rating does this solution have? b. Find the weekly diet that meets the nutritional requirements with the highest pref- erence rating. What preference rating does this solution have? What cost is associ- ated with this solution? c. Find the solution that minimizes the maximum percentage deviation from the opti- mum values for each individual objective. What cost and preference rating is asso- ciated with this solution? d. 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 asso- ciated with this solution? e. What other factors or constraints might you want to include in this analysis if you had to eat the resulting diet?
Polysat Fat 0.40 0.40 0.80 10.80 0.10 0.40 8.90 1.80 8.80 11.00 6.40 5.20 14.30 4.80 0.60 1 Weekly 2 Food Units 3 1 Potatoes 0 4 2 High-Nutrient Vegetables 5 3 Other Vegetables 5 4 Mixdures, mostly vegetable 7 5 Vitamin-C-rich fruits 8 6 other fruit 9 7 Whole-grain/high-fiber breakfast cereale 10 8 Other cereals 11 9 Whole-grain high-fiber flour meal, rice 12 10 Other flour meal rice pasta 13. 11 Whole grain/high fiber bread 14 12 Other breads 15 13 Bakery products 16.14 Grain mixtures 17 15 Milk, yogurt 18 18 Cheese 19 17 Cream, matures mostly milk 2018 Lower-cost red meats, variety meats 21 19 Higher-cost ted meats, variety meats 22 20 Poultry 23 21 Fish shellfish 24 22 Bacon sausage, luncheon meats 25 23 Eggs 26 24 Dry beans. peas, lentils 27 25. Mastures, mostly meat poultry, fish, ego 28 26 Nuts, peanut butter 29 27 Fats Oils 30 28 Sugar, sweets 31 29 Seasonings 32 30 Soft drinks, punches, ades 33 31 Coffee, tea 34 Weekdy Total Weekdy Lower Limit Weekly Upper Limit Carbo hydrates Total Fat 93.80 260 30 80 100 37 10 200 174.40 101.00 81.90 070 71.40 1.80 323.60 21 90 382 30 6.20 32850 17 90 346.00 6.20 217 10 14.90 225.10 18.60 300 40 69.10 196 80 25.10 32 00 1480 10.50 134 40 107.30 60 50 1.30 84.90 0.60 7400 0.40 42.10 2.40 1270 7.60 170.40 4.90 40.10 235 60 5.00 58.40 37.70 88.80 22170 14 80 37000 406.90 7:30 36.30 5.50 58.40 0.00 87.70 170 . 0.00 0.00 9999 676.67 Saturated Fat 1.10 0.10 0.40 26.10 000 0.30 4.60 250 2.70 120 2.60 4.30 21.50 9.50 9.30 8515 41.80 33.60 28.30 1200 2.70 63.00 12.40 130 11.70 37.80 90 40 4.00 1.80 0.00 0.60 0 000 225 56 4.00 Monosat. Fats 0.80 0.10 0.50 21.10 0 10 0.30 6.90 110 4 30 2.30 3.70 7.10 27.20 8.60 4.10 38.30 13.50 37 10 3250 16.90 4 30 79.10 15 24 100 14 70 102 00 137 20 233 1.70 0.00 0.10 0 0.00 9999 Sugar 000 400 16.00 256.00 400 3200 140.00 392.00 8.00 52.00 4.00 16.00 392.00 24.00 400 0.00 256.00 0.00 0.00 0.00 400 16.00 0.00 44.00 20.00 56.00 24.00 1576.00 Choles. terol 200 0.00 000 0.00 0.00 0.00 0.00 0.00 0.00 5200 100 700 11200 6100 60.00 413.00 137.00 284 00 278.00 27100 17200 28700 1698.00 5.00 101.00 0.00 15200 3.00 0.00 0.00 000 . 0.00 2100 Cost per unit $0 391 $1.014 $0.958 $1.897 50 721 $0.981 $2770 $3327 $0.966 50 720 $1553 $1.111 $2.460 $1.556 $0 362 $2811 $1223 $1918 $2 801 $1281 $3.471 $2481 $0 838 $1.309 $1957 $2504 $1.198 $1.111 52077 $0 249 $6.018 $6.000 Pref. Rating 6.68 17.81 13 31 245 159 1488 8.22 9.43 44 0.28 5.52 49 903 25.67 17.34 22.72 17.1 44 58 89.24 57.53 78.18 1783 9.35 13.08 452 21 26 3.17 239 58 47 42 2.00 450 5.90 9.20 3.80 18.40 5.50 1.80 8.00 71.10 125 80 0.50 1 20 0.00 0.50 400 116.00 4.00 0 0.00 2436 0 0.00 9999
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 differ- ent food groups and determined the contributions a serving from each group makes to 24 different nutritional categories. A partial listing of this information is given in Figure 7.20 (and in the file DietData.xlsm that accompanies this book).

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