Fencing Optimization: Worked Example and Solution
A complete constrained one-variable optimization example with method choice, derivation, verification, and a common wrong approach.
1 problem8 min estimated timeIntermediate to advanced progression
Problem
- Use 240 m of fence for three sides of a riverside rectangle. Maximize area.
Complete worked solutions
Every problem has a source-matched answer and independently reviewed derivation.
01
Problem 1: Use 240 m of fence for three sides of a riverside rectangle. Maximize area.
Answer:
Why this method: Constrained one-variable optimization matches the mathematical structure before any algebraic cleanup.
- With 2x+y=240, A=x(240-2x); A'=240-4x=0.
- Check feasibility, endpoints, and the sign or second derivative before declaring the optimum.
- Therefore the result is .
What is included
See a concise answer and full derivation for use 240 m of fence for three sides of a riverside rectangle. maximize area.
Skills assessed
- Constrained one-variable optimization
Prerequisites
- derivative rules
- critical points
Long description
Read the diagram from top to bottom. Each numbered box names one decision or mathematical operation. Arrows show the required order; the text labels remain the complete interpretation in print, dark mode, and nonvisual reading.
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Common errors
- Solving f'(x)=0 without building the constraint or checking the feasible domain.