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### diet.R

# Copyright 2024, Gurobi Optimization, LLC
#
# Solve the classic diet model, showing how to add constraints
# to an existing model.

library(Matrix)
library(gurobi)

# display results
printSolution <- function(model, res, nCategories, nFoods) {
if (res$status == 'OPTIMAL') { cat('\nCost: ',res$objval,'\nBuy:\n')
for (j in nCategories + 1:nFoods) {
if (res$x[j] > 1e-4) { cat(format(model$varnames[j],justify='left',width=10),':',
format(res$x[j],justify='right',width=10,nsmall=2),'\n') } } cat('\nNutrition:\n') for (j in 1:nCategories) { cat(format(model$varnames[j],justify='left',width=10),':',
format(res$x[j],justify='right',width=10,nsmall=2),'\n') } } else { cat('No solution\n') } } # define primitive data Categories <- c('calories', 'protein', 'fat', 'sodium') nCategories <- length(Categories) minNutrition <- c( 1800 , 91 , 0 , 0 ) maxNutrition <- c( 2200 , Inf , 65 , 1779 ) Foods <- c('hamburger', 'chicken', 'hot dog', 'fries', 'macaroni', 'pizza', 'salad', 'milk', 'ice cream') nFoods <- length(Foods) cost <- c(2.49, 2.89, 1.50, 1.89, 2.09, 1.99, 2.49, 0.89, 1.59) nutritionValues <- c( 410, 24, 26 , 730, 420, 32, 10 , 1190, 560, 20, 32 , 1800, 380, 4, 19 , 270, 320, 12, 10 , 930, 320, 15, 12 , 820, 320, 31, 12 , 1230, 100, 8, 2.5, 125, 330, 8, 10 , 180 ) # Build model model <- list() model$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$constrnames <- Categories model$modelname   <- 'diet'
model$modelsense <- 'min' # Optimize res <- gurobi(model) printSolution(model, res, nCategories, nFoods) # Adding constraint: at most 6 servings of dairy # this is the matrix part of the constraint B <- spMatrix(1, nCategories + nFoods, i = rep(1,2), j = (nCategories+c(8,9)), x = rep(1,2)) # append B to A model$A           <- rbind(model$A, B) # extend row-related vectors model$constrnames <- c(model$constrnames, 'limit_dairy') model$rhs         <- c(model$rhs, 6) model$sense       <- c(model\$sense,       '<')

# Optimize
res <- gurobi(model)
printSolution(model, res, nCategories, nFoods)

# Clear space
rm(res, model)


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