The diet problem in GNU MathProg.

diet.data

set Foods := Rice Quinoa Tortilla Lentils Broccoli;
set NutrientTypes := Carbs Proteins Fat;

param Nutrients:
        Carbs  Proteins  Fat :=
Rice      53     4.4     0.4
Quinoa    40     8       3.6
Tortilla  12     3       2
Lentils   53     12      0.9
Broccoli   6     1.9     0.3
;

param Costs :=
Rice        0.5
Quinoa      0.9
Tortilla    0.1
Lentils     0.6
Broccoli    0.4
;

param Bounds: 1 2 :=
Carbs    100    1000
Proteins  10     100
Fat        0     100
;

end;

diet.model

set Foods;
set NutrientTypes;
param Nutrients{i in Foods, j in NutrientTypes};
param Costs{i in Foods};
param Bounds{i in NutrientTypes, j in 1..2};

var x{i in Foods} >= 0;

maximize protein: sum{i in Foods} Nutrients[i,'Proteins'] * x[i];

s.t.

bndConstr{k in NutrientTypes}:
    Bounds[k,1] <= sum{i in Foods} Nutrients[i,k] * x[i] <= Bounds[k,2];
costConstr:
    sum{i in Foods} Costs[i] * x[i] <= 2;

solve;
display protein;
display x;
end;