Nonlinear discrete optimization in R

Question

I have a simple (indeed standard in economics) nonlinear constrained discrete maximisation problem to solve in R and am having trouble. I found solutions for pa

Answer 1

I think this problem is very similar in nature to this question (Solve indeterminate equation system in R). The answer by Richie Cotton was the basis to this possible solution:

df <- data.frame(product=c("ananas","banana","cookie"),
                 price=c(2.17,0.75,1.34),stringsAsFactors = F)

FUN <- function(w, price=df$price){
  total <- sum(price * w) 
  errs <- c((total-20)^2, -(sqrt(w[1]) * sqrt(w[2]) * sqrt(w[3])))
  sum(errs)
}

init_w <- rep(10,3)
res <- optim(init_w, FUN, lower=rep(0,3), method="L-BFGS-B")
res
res$par # 3.140093 9.085182 5.085095
sum(res$par*df$price) # 20.44192

Notice that the total cost (i.e. price) for the solution is $ 20.44. To solve this problem, we can weight the error terms to put more emphasis on the 1st term, which relates to the total cost:

### weighting of error terms
FUN2 <- function(w, price=df$price){
  total <- sum(price * w) 
  errs <- c(100*(total-20)^2, -(sqrt(w[1]) * sqrt(w[2]) * sqrt(w[3]))) # 1st term weighted by 100
  sum(errs)
}

init_w <- rep(10,3)
res <- optim(init_w, FUN2, lower=rep(0,3), method="L-BFGS-B")
res
res$par # 3.072868 8.890832 4.976212
sum(res$par*df$price) # 20.00437