The Diet Problem

import org.ojalgo.OjAlgoUtils;
import org.ojalgo.netio.BasicLogger;
import org.ojalgo.optimisation.Expression;
import org.ojalgo.optimisation.ExpressionsBasedModel;
import org.ojalgo.optimisation.Optimisation;
import org.ojalgo.optimisation.Variable;

/**
 * An example of how to implement a simple optimisation problem - The Diet Problem. It's one of the earliest
 * real-life problems to be solved using linear programming.
 *
 * @see https://www.ojalgo.org/2019/05/the-diet-problem/
 * @see https://github.com/optimatika/ojAlgo/wiki/The-Diet-Problem
 */
public class TheDietProblem {

    public static void main(final String[] args) {

        BasicLogger.debug();
        BasicLogger.debug(TheDietProblem.class);
        BasicLogger.debug(OjAlgoUtils.getTitle());
        BasicLogger.debug(OjAlgoUtils.getDate());
        BasicLogger.debug();

        // Create a new model.
        ExpressionsBasedModel model = new ExpressionsBasedModel();

        // Add variables expressing servings of each of the considered foods
        // Set lower and upper limits on the number of servings as well as the weight (cost of a
        // serving) for each variable.
        Variable bread = model.newVariable("Bread").lower(0).upper(10).weight(0.05);
        Variable corn = model.newVariable("Corn").lower(0).upper(10).weight(0.18);
        Variable milk = model.newVariable("Milk").lower(0).upper(10).weight(0.23);

        // Create a vitamin A constraint.
        // Set lower and upper limits and then specify how much vitamin A a serving of each of the
        // foods contain.
        Expression vitaminA = model.newExpression("Vitamin A").lower(5000).upper(50000);
        vitaminA.set(bread, 0).set(corn, 107).set(milk, 500);

        // Create a calories constraint...
        Expression calories = model.newExpression("Calories").lower(2000).upper(2250);
        calories.set(bread, 65).set(corn, 72).set(milk, 121);

        // Solve the problem - minimise the cost
        Optimisation.Result result = model.minimise();

        // Print the result
        BasicLogger.debug();
        BasicLogger.debug(result);
        BasicLogger.debug();

        // Modify the model to require an integer valued solution.
        BasicLogger.debug("Adding integer constraints...");
        bread.integer(true);
        corn.integer(true);
        milk.integer(true);

        // Solve again
        result = model.minimise();

        // Print the result, and the model
        BasicLogger.debug();
        BasicLogger.debug(result);
        BasicLogger.debug();
        BasicLogger.debug(model);
        BasicLogger.debug();
    }

}