#!/usr/bin/env python3# Copyright 2025, Gurobi Optimization, LLC# Solve the classic diet model, showing how to add constraints# to an existing model.importgurobipyasgpfromgurobipyimportGRB# Nutrition guidelines, based on# USDA Dietary Guidelines for Americans, 2005# http://www.health.gov/DietaryGuidelines/dga2005/categories,minNutrition,maxNutrition=gp.multidict({"calories":[1800,2200],"protein":[91,GRB.INFINITY],"fat":[0,65],"sodium":[0,1779],})foods,cost=gp.multidict({"hamburger":2.49,"chicken":2.89,"hot dog":1.50,"fries":1.89,"macaroni":2.09,"pizza":1.99,"salad":2.49,"milk":0.89,"ice cream":1.59,})# Nutrition values for the foodsnutritionValues={("hamburger","calories"):410,("hamburger","protein"):24,("hamburger","fat"):26,("hamburger","sodium"):730,("chicken","calories"):420,("chicken","protein"):32,("chicken","fat"):10,("chicken","sodium"):1190,("hot dog","calories"):560,("hot dog","protein"):20,("hot dog","fat"):32,("hot dog","sodium"):1800,("fries","calories"):380,("fries","protein"):4,("fries","fat"):19,("fries","sodium"):270,("macaroni","calories"):320,("macaroni","protein"):12,("macaroni","fat"):10,("macaroni","sodium"):930,("pizza","calories"):320,("pizza","protein"):15,("pizza","fat"):12,("pizza","sodium"):820,("salad","calories"):320,("salad","protein"):31,("salad","fat"):12,("salad","sodium"):1230,("milk","calories"):100,("milk","protein"):8,("milk","fat"):2.5,("milk","sodium"):125,("ice cream","calories"):330,("ice cream","protein"):8,("ice cream","fat"):10,("ice cream","sodium"):180,}# Modelm=gp.Model("diet")# Create decision variables for the foods to buybuy=m.addVars(foods,name="buy")# You could use Python looping constructs and m.addVar() to create# these decision variables instead.  The following would be equivalent## buy = {}# for f in foods:#   buy[f] = m.addVar(name=f)# The objective is to minimize the costsm.setObjective(buy.prod(cost),GRB.MINIMIZE)# Using looping constructs, the preceding statement would be:## m.setObjective(sum(buy[f]*cost[f] for f in foods), GRB.MINIMIZE)# Nutrition constraintsm.addConstrs((gp.quicksum(nutritionValues[f,c]*buy[f]forfinfoods)==[minNutrition[c],maxNutrition[c]]forcincategories),"_",)# Using looping constructs, the preceding statement would be:## for c in categories:#  m.addRange(sum(nutritionValues[f, c] * buy[f] for f in foods),#             minNutrition[c], maxNutrition[c], c)defprintSolution():ifm.status==GRB.OPTIMAL:print(f"\nCost:{m.ObjVal:g}")print("\nBuy:")forfinfoods:ifbuy[f].X>0.0001:print(f"{f}{buy[f].X:g}")else:print("No solution")# Solvem.optimize()printSolution()print("\nAdding constraint: at most 6 servings of dairy")m.addConstr(buy.sum(["milk","ice cream"])<=6,"limit_dairy")# Solvem.optimize()printSolution()