Try our new documentation site.


diet.m


function diet()
% Copyright 2019, 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

Try Gurobi for Free

Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.

Evaluation License
Get a free, full-featured license of the Gurobi Optimizer to experience the performance, support, benchmarking and tuning services we provide as part of our product offering.
Academic License
Gurobi supports the teaching and use of optimization within academic institutions. We offer free, full-featured copies of Gurobi for use in class, and for research.
Cloud Trial

Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.

Search