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Optimizing the sheep pen
A Northumberland sheep farmer has two pieces of fencing, each 10m long, which she wants to fix to a straight stone wall to make a triangular sheep pen. What is the maximum area of the pen?
TI-Nspire offers a wide range of possible solutions to optimization problems like this and seven different approaches are discussed here. The notes, written primarily for teachers, provide innovative ideas that can be adapted for classroom use with a wide range of students.
The approaches are
- numeric (using both the Calculator application and a spreadsheet)
- graphic (scattergraphs and function plotting)
- symbolic (a brief look at using CAS - Computer Algebra System)
- geometric (providing insights into the shape of the sheep pen)
- statistic (analyzing data collected automatically)
- algorithmic (using the programming facilities of TI-Nspire)
- synoptic (summarising the various approaches on a Notes page)