Optimising Fences
applied
Another classic problem you could consider for your own garden.
Introduction
Look up this classic fencing problem. The challenge will be to make it personal, interesting and different to the solutions online. How could you graph it or use calculus to demonstrate a solution? Set a limit on the number of fence pieces you have and explore the associated mathematics.
Guiding Questions
- What is the objective function you want to optimize?
- What constraints apply to this problem?
- How can you use calculus to find maximum or minimum values?
- Can you verify your solution is optimal rather than a local extremum?
- How sensitive is the optimal solution to changes in parameters?
Key Mathematical Concepts
Optimization
Calculus
Constraints
Perimeter and Area