# Copyright 2025, Gurobi Optimization, LLC## Solve the classic diet model, showing how to add constraints# to an existing model.library(Matrix)library(gurobi)# display resultsprintSolution<-function(model,res,nCategories,nFoods){if(res$status=='OPTIMAL'){cat('\nCost: ',res$objval,'\nBuy:\n')for(jinnCategories+1:nFoods){if(res$x[j]>1e-4){cat(format(model$varnames[j],justify='left',width=10),':',format(res$x[j],justify='right',width=10,nsmall=2),'\n')}}cat('\nNutrition:\n')for(jin1:nCategories){cat(format(model$varnames[j],justify='left',width=10),':',format(res$x[j],justify='right',width=10,nsmall=2),'\n')}}else{cat('No solution\n')}}# define primitive dataCategories<-c('calories','protein','fat','sodium')nCategories<-length(Categories)minNutrition<-c(1800,91,0,0)maxNutrition<-c(2200,Inf,65,1779)Foods<-c('hamburger','chicken','hot dog','fries','macaroni','pizza','salad','milk','ice cream')nFoods<-length(Foods)cost<-c(2.49,2.89,1.50,1.89,2.09,1.99,2.49,0.89,1.59)nutritionValues<-c(410,24,26,730,420,32,10,1190,560,20,32,1800,380,4,19,270,320,12,10,930,320,15,12,820,320,31,12,1230,100,8,2.5,125,330,8,10,180)# Build modelmodel<-list()model$A<-spMatrix(nCategories,nCategories+nFoods,i=c(mapply(rep,1:4,1+nFoods)),j=c(1,(nCategories+1):(nCategories+nFoods),2,(nCategories+1):(nCategories+nFoods),3,(nCategories+1):(nCategories+nFoods),4,(nCategories+1):(nCategories+nFoods)),x=c(-1.0,nutritionValues[1+nCategories*(0:(nFoods-1))],-1.0,nutritionValues[2+nCategories*(0:(nFoods-1))],-1.0,nutritionValues[3+nCategories*(0:(nFoods-1))],-1.0,nutritionValues[4+nCategories*(0:(nFoods-1))]))model$obj<-c(rep(0,nCategories),cost)model$lb<-c(minNutrition,rep(0,nFoods))model$ub<-c(maxNutrition,rep(Inf,nFoods))model$varnames<-c(Categories,Foods)model$rhs<-rep(0,nCategories)model$sense<-rep('=',nCategories)model$constrnames<-Categoriesmodel$modelname<-'diet'model$modelsense<-'min'# Optimizeres<-gurobi(model)printSolution(model,res,nCategories,nFoods)# Adding constraint: at most 6 servings of dairy# this is the matrix part of the constraintB<-spMatrix(1,nCategories+nFoods,i=rep(1,2),j=(nCategories+c(8,9)),x=rep(1,2))# append B to Amodel$A<-rbind(model$A,B)# extend row-related vectorsmodel$constrnames<-c(model$constrnames,'limit_dairy')model$rhs<-c(model$rhs,6)model$sense<-c(model$sense,'<')# Optimizeres<-gurobi(model)printSolution(model,res,nCategories,nFoods)# Clear spacerm(res,model)