Optimization in R using constraints - r

Question

I have some problems setting up an optimalization process using R. My data set is as follows:
set.seed(123)
library(lpSolve)
num_data <- 1000
bal_max <- .2/100
ind_max <- 10.5/100
data <- data.frame(id = 1:num_data,
balance = pmax(0,runif(num_data, 0, 1000)),
industry = rep(seq(1:10),num_data/10))
data$risk <- pmax(0, data$balance + rnorm(num_data,100,10))
As you can see, there are 1000 ids, 10 different industries. The objective is to maximize the sum of column "risk" and at the same time make sure that the fraction of each individual loan and industry cannot be above respectively 2% and 10.5%.
In the current data set these conditions are not met:
max(data$balance) / sum(data$balance)
#[1] 0.002009751
industry <- aggregate(balance ~ industry, FUN=sum,data=data)
max(industry$balance) / sum(industry$balance)
#[1] 0.1093997
Thus before we can maximize the column risk, these two conditions needs to be met. The remainder of my code is as follows
# set up linear prog problem
num_x <- nrow(data)
num_ind <- length(unique(data$industry))
objective.in <- data$risk
# define quantity to be maximized
# construct right-hand-side of constraint vector
# - sum of balances = 1
# - each balance <= bal_max
# - sum of balances for each industry <= ind_max
# - lp solver function imposes constraint that each balance >= 0
const.rhs <- c( 1, rep(bal_max, num_x), rep(ind_max, num_ind))
# construct constraint matrix for same constraints
mat_ind <- matrix(0,nrow=num_ind, ncol=num_x)
for( i in 1:num_ind) mat_ind[i,which(data$industry == i)] <- 1
const.mat <- rbind( matrix(1, nrow=1,ncol=num_x), diag(num_x), mat_ind )
# define directions for each constraint equation
const.dir <- c("=", rep("<=",num_x), rep("<=", num_ind))
# find balances for max risk
#
max_risk <- lp(direction="max", objective.in=objective.in, const.mat=const.mat,
const.dir=const.dir, const.rhs=const.rhs)
max_risk
# add data balances with optimum solution
data$balance <- max_risk$solution
# each balance should be smaller than bal_max
max(data$balance)
# industry should be smaller than 10.5% each
industry <- aggregate(balance ~ industry, FUN=sum,data=data)
industry
As you can see each industry and individual id does not exceed the bounderies (10.5% and 2%) anymore. The problem is that this code either fills in 2% or 0% for each loanid (such that the sum is 1). However, the absolute value of the initial balance should not rise as well. In this example the original balances often rises (fills in 2%).
In short, I want to optimize the column "risk" where each individual ID is capped at 2% of the total balance (after the optimalization process) and each industry is capped at 10.5% (after the optimalization process) of the total balance. The sum of all fractions should be one and the absolute value of the balance cannot increase.
The idea is to decrease the balances such that all conditions are met and "risk" is optimized.