diet.gms : Stigler's Nutrition Model
This model determines a least cost diet which meets the daily
allowances of nutrients for a moderately active man weighing 154 lbs.
Reference:
- Dantzig, G B, Chapter 27.1. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.
Small Model of Type: LP
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$Title Stigler's Nutrition model (DIET,SEQ=7)
$Ontext
This model determines a least cost diet which meets the daily
allowances of nutrients for a moderately active man weighing 154 lbs.
Dantzig, G B, Chapter 27.1. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
$Offtext
Sets n nutrients / calorie thousands , protein grams , calcium grams , iron milligrams
vitamin-a thousand ius, vitamin-b1 milligrams, vitamin-b2 milligrams,
niacin milligrams , vitamin-c milligrams /
f foods / wheat , cornmeal , cannedmilk, margarine , cheese , peanut-b , lard
liver , porkroast, salmon , greenbeans, cabbage , onions , potatoes
spinach, sweet-pot, peaches , prunes , limabeans, navybeans /
Parameter b(n) required daily allowances of nutrients / calorie 3, protein 70 , calcium .8 , iron 12
vitamin-a 5, vitamin-b1 1.8, vitamin-b2 2.7,
niacin 18, vitamin-c 75 /
Table a(f,n) nutritive value of foods (per dollar spent)
calorie protein calcium iron vitamin-a vitamin-b1 vitamin-b2 niacin vitamin-c
* (1000) (g) (g) (mg) (1000iu) (mg) (mg) (mg) (mg)
wheat 44.7 1411 2.0 365 55.4 33.3 441
cornmeal 36 897 1.7 99 30.9 17.4 7.9 106
cannedmilk 8.4 422 15.1 9 26 3 23.5 11 60
margarine 20.6 17 .6 6 55.8 .2
cheese 7.4 448 16.4 19 28.1 .8 10.3 4
peanut-b 15.7 661 1 48 9.6 8.1 471
lard 41.7 .2 .5 5
liver 2.2 333 .2 139 169.2 6.4 50.8 316 525
porkroast 4.4 249 .3 37 18.2 3.6 79
salmon 5.8 705 6.8 45 3.5 1 4.9 209
greenbeans 2.4 138 3.7 80 69 4.3 5.8 37 862
cabbage 2.6 125 4 36 7.2 9 4.5 26 5369
onions 5.8 166 3.8 59 16.6 4.7 5.9 21 1184
potatoes 14.3 336 1.8 118 6.7 29.4 7.1 198 2522
spinach 1.1 106 138 918.4 5.7 13.8 33 2755
sweet-pot 9.6 138 2.7 54 290.7 8.4 5.4 83 1912
peaches 8.5 87 1.7 173 86.8 1.2 4.3 55 57
prunes 12.8 99 2.5 154 85.7 3.9 4.3 65 257
limabeans 17.4 1055 3.7 459 5.1 26.9 38.2 93
navybeans 26.9 1691 11.4 792 38.4 24.6 217
Positive Variable x(f) dollars of food f to be purchased daily (dollars)
Free Variable cost total food bill (dollars)
Equations nb(n) nutrient balance (units), cb cost balance (dollars) ;
nb(n).. sum(f, a(f,n)*x(f)) =g= b(n); cb.. cost=e= sum(f, x(f));
Model diet stiglers diet problem / nb,cb /;
Solve diet minimizing cost using lp;
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