Optimizing given constraints: The Electric Power Market - r

Question

I took a class a few years ago about power market optimization and tried building a small example in R that I have worked up the courage to tackle again. However I need some help.
I would like to take the constraints of ~4 power plants and try to satisfy a single location's demand for power, as well as demand for 3 other types of ancillary services needed in the power market (called Reserves). I am looking to minimize the total cost of the generators of electricity.
I've laid out a lot of information but can't seem to figure out to how to start using any optimization packages (I have used optim before but couldn't quite work with these constraints). This will be a little lengthy but I'm using comments in R code for an easy copy-paste-run for those interested in helping or viewing what I have.
Warning: You're going to learn more about power plants and electricity markets than you want to from this post.
#####-------------------------------
# G for GENERATOR No.
# For each generator we have the following data:
## Maximum Capacity: the most power it can be producing
## Technical Minimum Capacity: the smallest amount (other than being off)
## Cost per Megawatt: The cost of generating power ($/MW)
## Ramp Rate: The speed a plant can change to a higher or lower output (MW/min)
G1 <- c(200, 100, 50, 2)
G2 <- c(150, 10, 80, 10)
G3 <- c(200, 100, 55, 2)
G4 <- c(150, 10, 85, 10)
Gdat.1 <- rbind(G1,G2,G3,G4)
colnames(Gdat.1) = c("MWMax","MWMin","Cost","RampRate")
Gdat.1
n <- nrow(Gdat.1) # number of generators
#####-------------------------------
# System Requirements: Demand
## Supply (MW) must equal demand.
Demand <- 415
# System Requirements: Reserves
## Total Reserves of the system must be met.
### R1: Primary Reserves
##### 0.5 minute response time, bi-direcitonal (Ramp UP/DOWN)
### R2: Secondary Reserves
##### 5 minute response time, bi-directional (Ramp UP/DOWN)
### R3: Tertiary Reserves
##### 15 minute response time, uni-directional (Ramp UP only)
# R for Reserve Type.
# For each Reserve Type we have the following data:
# Total: MW Needed
# minutes: within how much time the MW is needed by
# bid: amount the operator will pay for MW reserves $/MW)
R1 <- c(2, 0.5, 60) # Primary
R2 <- c(8, 5, 40) # Secondary
R3 <- c(20, 15, 0) # Tertiary
Reserves <- rbind(R1,R2,R3)
colnames(Reserves) = c("Total","Minutes","Bid")
Reserves
#####-------------------------------
## Ramp Rate constraint of generators
### For R1 (Primary Reserves) the system needs 2 MW that can be supplied 30 seconds,
### a Generator with a ramprate of 2 MW/min will only be able to supply
### 1 MW for primary reserves, while a Generator with a ramprate of 10 MW/min
### will be able to supply 5 MW.
# How much each Generator can supply in the time time
R1max <- Gdat.1[,"RampRate"] * Reserves["R1","Minutes"]
R2max <- Gdat.1[,"RampRate"] * Reserves["R2","Minutes"]
R3max <- Gdat.1[,"RampRate"] * Reserves["R3","Minutes"]
R1min <- -R1max # recall, bi-directional
R2min <- -R2max # bi-directional
R3min <- 0/R3max # uni-direction up
# we no longer need RampRate since we used it to calculate
Gdat <- cbind(Gdat.1[,-4], cbind(R1max,R2max,R3max,R1min,R2min,R3min))
#####-------------------------------
# Now we initialize each generator's commitments that can change during optimization
MW.Demand = rep(0,n) # general MW to satisfy demand
MW.R1 = rep(0,n) # MW to satisfy Primary Reserves
MW.R2 = rep(0,n) # MW to satisfy Secondary Reserves
MW.R3 = rep(0,n) # MW to satisfy Tertiary Reserves
Commit.orig <- cbind(MW.Demand,MW.R1,MW.R2,MW.R3)
rownames(Commit.orig) <- paste0("G",seq(1,n))
Commit <- Commit.orig
# Some initial guess (may be exactly the right answer...)
Commit <- matrix(c(200,0,0,0,
17.5,1,6.5,20,
197.5,1,1.5,0,
0,0,0,0), 4, 4, byrow = T, dimnames(Commit.orig))
#####-------------------------------
# Objective Function, cost per MW of each generator times their total MW output
# minimize the total cost, not sure which way to list it, or if this way even works
sum(Commit * Gdat[,"Cost"])
sum(Gdat[,"Cost"] %*% Commit)
sum(rowSums(Ctest * Gdat[,"Cost"]))
#####-------------------------------
# Constraints
sum(Commit[,"MW.Demand"]) == Demand & # All generators together must sum to meet system demand requirements
sum(Commit[,"MW.R1"]) == Reserves["R1","Total"] & # Total Primary Reserves are met
sum(Commit[,"MW.R2"]) == Reserves["R2","Total"] & # Total Secondary
sum(Commit[,"MW.R3"]) == Reserves["R3","Total"] & # Total Tertiary
(rowSums(Commit) <= Gdat[,"MWMax"] | rowSums(Commit) == 0) & # Generators must be less than or equal to its max, or off
(rowSums(Commit) >= Gdat[,"MWMin"] | rowSums(Commit) == 0) & # Genreators must be more than or equal to its min, or off
Commit[,"MW.R1"] <= Gdat[,"R1max"] & Commit[,"MW.R1"] >= Gdat[,"R1min"] & # Genrators cannot exceed ramprate limitations
Commit[,"MW.R2"] <= Gdat[,"R2max"] & Commit[,"MW.R2"] >= Gdat[,"R2min"] & # - for the bi-directional
Commit[,"MW.R3"] <= Gdat[,"R3max"] & Commit[,"MW.R3"] >= Gdat[,"R3min"] # - or unidirectional reserves
Thank you anyone willing to take a look at this.