R lpsolver manufacturing optimization. Need help distributing volume and with constraint matrix

Question

I'd like to start using {lpsolve} in R to solve some manufacturing- optimization problems. I've set up a few examples but haven't been able to get them to work.

Here is an example I set up and the code I've been messing with: Any help or direction would be greatly appreciated. I'm generally confused when it comes to the constraint matrix.

Problem description: I'm trying to distribute the three different products across the three tools in order to minimize production time across all three.

library("lpSolve")
# Define problem data 
products <- c("q1", "q2", "q3") 
volumes <- c(20, 40, 1000) 
tools <- c("A", "B", "C") 
build_time <- c(15,20,25) 


# Define objective function coefficients 
obj_func <- c(build_time)

# matrix
const.mat <- rbind(
  c(20, 40, 1000)
)

dir <- c(">=", ">=", ">=") 
rhs <- c(sum(volumes)) 

result <- lp("min", obj_func, const.mat, dir, rhs, all.bin = TRUE)

# Print solution 
print(result$solution) 

# Calculate time required for each tool 
time_required <- build_time * result$solution * volumes 
names(time_required) <- tools 
print(time_required)