We are in a drought (well, we were), but people keep watering their lawns. The water company wants to know how much water it will need to supply. On average, the lawns in this city need 1 million gallons per day. IF it rains on any given day, the rain might supply up to 2 million gallons per day (assume if it rains, a uniform distribution from >0 to <=2 Mgal). On average, rain in the drought supplies only 5 million gallons per month. Rain at a rate of more than what the lawns need runs off into the sewer and cannot be reclaimed or used.
Part 1A (4 pts): Use this information to produce a simulation to determine how much the water utility must purchase for the next 3 months. The simulation must be user-friendly.
Part 1B (2 pts): Run your simulation a number of times and interpret the statistics. How much should the utility purchase each month to guarantee a service level of 90%?
Part 2A (3 pts): The town is stepping up enforcement of watering violations. 90% of the people each month who violate watering restrictions get away with it (Freebirds). Of those who get caught (Jailbirds), 80% won’t do it again (and become Angels). Angels are rarely tempted to violate the restrictions next month (5%). Build a Markov Process model using these three states and given 50% of the town is estimated to initially be Angels, is the policing effective? What percentage of the population violates restrictions after 10 months?
Part 2B (3 pts): Run your Markov model to determine which is more effective: Policing to catch 20% of the violators each month or public service announcements to reduce the Angel temptation rate to 3%.
For each of these activities you need to provide the model and a SHORT writeup defining variables and results. No model without annotation.