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diet.m
function diet()
% Copyright 2023, Gurobi Optimization, LLC
%
% Solve the classic diet model
% Nutrition guidelines, based on
% USDA Dietary Guidelines for Americans, 2005
% http://www.health.gov/DietaryGuidelines/dga2005/
ncategories = 4;
categories = {'calories'; 'protein'; 'fat'; 'sodium'};
% minNutrition maxNutrition
categorynutrition = [ 1800 2200; % calories
91 inf; % protein
0 65; % fat
0 1779]; % sodium
nfoods = 9;
foods = {'hamburger';
'chicken';
'hot dog';
'fries';
'macaroni';
'pizza';
'salad';
'milk';
'ice cream'};
foodcost = [2.49; % hamburger
2.89; % chicken
1.50; % hot dog
1.89; % fries
2.09; % macaroni
1.99; % pizza
2.49; % salad
0.89; % milk
1.59]; % ice cream
% calories protein fat sodium
nutritionValues = [ 410 24 26 730; % hamburger
420 32 10 1190; % chicken
560 20 32 1800; % hot dog
380 4 19 270; % fries
320 12 10 930; % macaroni
320 15 12 820; % pizza
320 31 12 1230; % salad
100 8 2.5 125; % milk
330 8 10 180]; % ice cream
nutritionValues = sparse(nutritionValues);
model.modelName = 'diet';
% The variables are layed out as [ buy; nutrition]
model.obj = [ foodcost; zeros(ncategories, 1)];
model.lb = [ zeros(nfoods, 1); categorynutrition(:, 1)];
model.ub = [ inf(nfoods, 1); categorynutrition(:, 2)];
model.A = [ nutritionValues' -speye(ncategories)];
model.rhs = zeros(ncategories, 1);
model.sense = repmat('=', ncategories, 1);
function printSolution(result)
if strcmp(result.status, 'OPTIMAL')
buy = result.x(1:nfoods);
nutrition = result.x(nfoods+1:nfoods+ncategories);
fprintf('\nCost: %f\n', result.objval);
fprintf('\nBuy:\n')
for f=1:nfoods
if buy(f) > 0.0001
fprintf('%10s %g\n', foods{f}, buy(f));
end
end
fprintf('\nNutrition:\n')
for c=1:ncategories
fprintf('%10s %g\n', categories{c}, nutrition(c));
end
else
fprintf('No solution\n');
end
end
% Solve
results = gurobi(model);
printSolution(results);
fprintf('\nAdding constraint at most 6 servings of dairy\n')
milk = find(strcmp('milk', foods));
icecream = find(strcmp('ice cream', foods));
model.A(end+1,:) = sparse([1; 1], [milk; icecream], 1, ...
1, nfoods + ncategories);
model.rhs(end+1) = 6;
model.sense(end+1) = '<';
% Solve
results = gurobi(model);
printSolution(results)
end
