Your diet must provide minimum amounts of the following items: calories, calcium, vitamin A, riboflavin, and ascorbic acid. Your daily requirement for these items (in the above order) may be determined by reading off the numerical values corresponding to the first five letters of your name on Table 1. The following are the units used: 10 calories, 10 grams, 103 international units, milligrams, and 10 milligrams. Your choice of foods is somewhat limited because you find it financially advantageous to trade at a discount store that has little imagination. You can buy: (1) wheat flour (enriched), (2) evaporated milk, (3) cheddar cheese, (4) beef liver, (5) cabbage, (6) spinach, (7) sweet potatoes, (8) lima beans (dried). The nutritional values per dollar spent have been tabulated by Dantzig in Table 2. In addition, the store features a greyish powder, (9) Product X, sold in bulk, whose nutritional values per unit cost are also given in Table 1. The units (same order of items as before) are 10 calories/dollar, 10 grams/dollar, 10 international units/dollar, 10- milligrams/dollar, milligrams/dollar. Your doctor has coded your diet requirements and the nutritional properties of Product X under the first five letters of your name in Table 1. A B Diet 7 60 83 D 10 E 39 F 59 Table 1 X 63 N 6 52 0 10 Diet X 91 45 59 P 32 82 85 Q 51 98 47 67 97 82 R 58 S 20 50 69 U T 66 28 78 54 44 V 81 33 26 W 81 59 61 30 X 61 0 86 G 38 H 30 I 65 J 27 K 91 L 68 43 Y M 49 90 Z Table 2 Commodity 1. Wheat flour (enriched) 5. Com meal 15. Evaporated milk (can) 17. Oleomargarine 19. Cheese (cheddar) 21. Peanut butter 24. Lard 30. Liver (beef) 34. Pork loin roast 39 83 15.7 41.7 a) Find your minimum-cost diet and its cost. b) How much would you be willing to pay for pure vitamin A? pure riboflavin? c) By how much would the cost of lima beans have to change before it would enter (or leave, as the case may be) your diet? 2.2 4 d) Over what range of values of cost of beef liver would your diet contain this wonderful food? Calories Protein Calcium Iron Vitamin A Thiamine Riboflavin Niacin (1000) (grams) (grams) (mg.) (1000 IU) (mg.) 55.4 44:7 1411 2:0 365 897 1.7 99 422 15.1 36.0 8.4 9 6 6 20.6 17 7.4 448 661 e) Suppose the cost of foods 1, 3, 5, 7, and 9 went up 10%. How much would you be willing to pay for pure vitamin A? pure riboflavin? f) If the wheat flour were enriched by 10 units of vitamin A without additional cost, would this change your diet? g) A new food has come out (called GLUNK) having nutritional values per dollar of 83, 17, 25, 93, 07 (values are in the same order as for Product X). Would you want to include the new food in your diet? ASSE 333 .6 16.4 1.0 2 3 6.8 3.7 125 4.0 166 336 106 138 139 4.4 37 4.4 5.8 45 2.4 80 2.6 36 60 5.8 59 14.3 118 1.1 138 06 9.6 2.7 54 8.5 87 1.7 173 12.8 99 2.5 154 17.4 3.7 459 1055 26.9 1691 11.4 792 249 705 138 6 19 48 3.8 1.8 30.9 26.0 55.8 28.1 4 169.2 3.5 69.0 7.2 17.4 3.0 2 2 16.6 6.7 918.4 290.7 86.8 85.7 5.1 8 .8 9.6. T 6.4 18.2 1.0 4.3 9.0 4.7 29.4 27 5.7 8.4 1.2 3.9 26.9 38.4 10.3 8.1 (mg.) (mg.) (mg.) 33.3 441 7.9 106 235 23.5 11 5 40. Salmon, pink (can) 45. Green beans 46. Cabbage PASE 50. Onions 51. Potatoes PANT 52. Spinach 53. Sweet potatoes 64. Peaches, dried 65. Prunes, dried 68. Lima beans, dried 69. Navy beans, dried Source: G. B. Dantzig, Linear Programming and Extension, Princeton University Press, Princeton. N.J., 1963. 4 471 5 50.8 3.6 4.9 209 37 X 26 5.8 4.5 316 79 13.8 5.4 4.3 5.9 21 7.1 198 - 33 92 83 55 Ascorbic 4.3 38.2 24.6 217 65 93 15xIIIIllgll