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