# Gasoline Usage

Meet two of my favorite people: Gabbi and Govinda Tamburino. After years of careful planning, they committed to a life on the road and purchased a truck and Airstream travel trailer.

These two are incredibly responsible adults when it comes to finances, and they did their best to over-budget to be safe. Now, almost a year after their life-changing decision, they have a more complete (but ever-evolving) sense of how their routine finances play out.

But there are simply so many variables with so many uncertainties. Gas prices differ from state to state. Fuel economy differs depending on elevation, towing load, and incline. There's an element of spontaneity to their traveling, so distances between sites are (and have been) all over the place.

Also wildly variable is how far they will be from the nearest town. They both work remotely and cannot reliably predict the service they'll be able to get in order to have meetings with clients.

With all this in mind, how can we get a better picture of their expected budget for gasoline? It is one of their most common purchases, so knowing a range of values can help budget for everything more accordingly. We want to provide Gabbi and Govinda with a deeper understanding of their future finances.

## Translating This to MATHEMATICS

I wrote a program to easily tweak assumptions and get visual feedback. As Gabbi and Govinda fed me information, I played with the sliders until they verified that the graphs on screen looked reasonable. The heights represent how likely a scenario is relative to others.

### Below you'll see some screen Captures of this process.

Trip Frequency

The legal limit is 14 days, sometimes they leave as early as 10. Since there is no particular preference, the distribution is uniform on the left. On the right, we see Govinda's description translated into "days between trips" being on average 2-3.

Distance

On the left, we see long distances between sites when traveling. On the right, a range of shorter trip lengths based on how far away town is.

Fuel Economy

It is much worse when towing (left) than when driving into town (right).

Putting it all together.

Once we factor in the uncertain gas prices in a similar manner, we can see that on average, they can expect to pay around $75 per month (which I found out lined up quite well with their recent spending). However, looking at the distribution of gas prices, we can see there are situations that exist where they can spend as little as half that. There may also be months where they need to budget considerably more. ## Where Does this go From Here? What we have just done is perform a "risk assessment" by solving a "forward problem" under uncertainty. To understand the scenarios that lead to a particular dollar range being spent, we must solve an "inverse problem," which can help inform decisions. For example, lets say Gabbi or Govinda have a project that requires frequent travel into town, but they want to stay at a$50-85 range for the monthly gas budget. We would solve an inverse problem to describe how close to town they would have to find a site, or how good the fuel economy would have to be to pull that off.

Such information might inform their decision to park their trailer outside a friend's home in a neighboring town instead of somewhere at elevation. We rule out particular campsites based solely on distance.

The question will inform the inverse problem that is posed and solved, so we conclude this case study with the forward problem since it is more cut-and-dry. Hopefully this example demonstrated just some of the possible benefits that come out of applying computational mathematics to decision making.

Why should corporations be the only ones with such tools?

Should my friends not benefit from the same precise information?

Remember, good things come when you

Mind the Math.