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99 lines
3.5 KiB
99 lines
3.5 KiB
# STIGLER'S NUTRITION MODEL
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#
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# This model determines a least cost diet which meets the daily
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# allowances of nutrients for a moderately active man weighing 154 lbs.
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#
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# References:
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# Dantzig G B, "Linear Programming and Extensions."
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# Princeton University Press, Princeton, New Jersey, 1963,
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# Chapter 27-1.
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set N;
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/* nutrients */
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set F;
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/* foods */
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param b{N};
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/* required daily allowances of nutrients */
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param a{F,N};
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/* nutritive value of foods (per dollar spent) */
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var x{f in F} >= 0;
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/* dollars of food f to be purchased daily */
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s.t. nb{n in N}: sum{f in F} a[f,n] * x[f] = b[n];
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/* nutrient balance (units) */
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minimize cost: sum{f in F} x[f];
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/* total food bill (dollars) */
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data;
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param : N : b :=
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Calorie 3 /* thousands */
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Protein 70 /* grams */
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Calcium 0.8 /* grams */
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Iron 12 /* milligrams */
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Vitamin-A 5 /* thousands IUs */
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Vitamin-B1 1.8 /* milligrams */
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Vitamin-B2 2.7 /* milligrams */
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Niacin 18 /* milligrams */
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Vitamin-C 75 /* milligrams */ ;
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set F := Wheat Cornmeal Cannedmilk Margarine Cheese Peanut-B Lard
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Liver Porkroast Salmon Greenbeans Cabbage Onions Potatoes
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Spinach Sweet-Pot Peaches Prunes Limabeans Navybeans;
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param a default 0
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: Calorie Protein Calcium Iron Vitamin-A Vitamin-B1 :=
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# (1000) (g) (g) (mg) (1000IU) (mg)
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Wheat 44.7 1411 2.0 365 . 55.4
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Cornmeal 36 897 1.7 99 30.9 17.4
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Cannedmilk 8.4 422 15.1 9 26 3
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Margarine 20.6 17 .6 6 55.8 .2
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Cheese 7.4 448 16.4 19 28.1 .8
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Peanut-B 15.7 661 1 48 . 9.6
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Lard 41.7 . . . .2 .
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Liver 2.2 333 .2 139 169.2 6.4
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Porkroast 4.4 249 .3 37 . 18.2
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Salmon 5.8 705 6.8 45 3.5 1
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Greenbeans 2.4 138 3.7 80 69 4.3
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Cabbage 2.6 125 4 36 7.2 9
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Onions 5.8 166 3.8 59 16.6 4.7
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Potatoes 14.3 336 1.8 118 6.7 29.4
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Spinach 1.1 106 . 138 918.4 5.7
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Sweet-Pot 9.6 138 2.7 54 290.7 8.4
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Peaches 8.5 87 1.7 173 86.8 1.2
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Prunes 12.8 99 2.5 154 85.7 3.9
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Limabeans 17.4 1055 3.7 459 5.1 26.9
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Navybeans 26.9 1691 11.4 792 . 38.4
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: Vitamin-B2 Niacin Vitamin-C :=
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# (mg) (mg) (mg)
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Wheat 33.3 441 .
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Cornmeal 7.9 106 .
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Cannedmilk 23.5 11 60
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Margarine . . .
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Cheese 10.3 4 .
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Peanut-B 8.1 471 .
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Lard .5 5 .
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Liver 50.8 316 525
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Porkroast 3.6 79 .
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Salmon 4.9 209 .
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Greenbeans 5.8 37 862
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Cabbage 4.5 26 5369
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Onions 5.9 21 1184
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Potatoes 7.1 198 2522
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Spinach 13.8 33 2755
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Sweet-Pot 5.4 83 1912
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Peaches 4.3 55 57
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Prunes 4.3 65 257
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Limabeans 38.2 93 .
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Navybeans 24.6 217 . ;
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end;
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