I think we should be teaching optimization word problems in math class to kids sooner than we think (closer to 10…not starting at 16 years old…Perhaps even sooner).
Optimization word problems incorporate **proportionality, probability, and feedback loops** into a framework that is both practical and metaphorically powerful. In other words: useful. Its practicality ranges from personal health and finance to time management/resource allocation and scaling a business.
**Optimization Problem Example:**
**Problem:** You are planning a road trip with friends and want to minimize **total cost** (including fuel and snacks) while balancing **time constraints** and **uncertainty around fuel efficiency** due to variable road conditions.
The constraints are:
1. The trip distance is **500 miles**.
2. Your car averages **25 miles per gallon (mpg)**, but this may vary between **20-30 mpg** due to weather and traffic.
3. Gas costs **$4 per gallon**, and you expect to spend **$2 per hour** on snacks during driving and rest stops.
4. You must rest for **30 minutes after every 3 hours of driving** to avoid fatigue.
5. Your average driving speed is **60 miles per hour (mph)**.
6. You have a maximum of **10 hours** for the trip, including rest stops.
How can you minimize the total cost of the trip, including fuel and snacks, while adhering to the time constraint of 10 hours and accounting for uncertainty in fuel efficiency due to variable road conditions?