# Load packages
library(deSolve)
library(ggplot2)

# Define parameters
init_volume <- 100  # Initial volume of tank in litres
outflow <- c(1,1,2,1,2,2,1,1,1,2)  # Outflow (litres/hour) for each hour
times <- seq(0, 9, by = 1)  # Simulation time in hours

# Define tank model function
tank_model <- function(time, volume, parameters) {
  dV <- -parameters["outflow"][time+1]  # Change in volume is equal to the outflow rate
  return(list(dV))
}

# Set up initial conditions and run simulation
init_state <- c(V = init_volume)  # Initial state of the tank
parameters <- list(outflow = outflow)  # Parameters for the simulation

out <- ode(y = init_state, times = times, func = tank_model, parms = parameters)

# Plot tank volume over time and save as PDF file
pdf("tank_volume_plot.pdf")  # Specify PDF file name
ggplot(data = data.frame(time = out[,1], volume = out[,2])) +
  geom_line(aes(x = time, y = volume)) +
  labs(title = "Tank Volume Over Time", x = "Time (hours)", y = "Volume (litres)")
dev.off()  # Close PDF device