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Constrained Optimization

Constrained Optimization
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2015-10-15 03:19
FunctionCalculusOptimization
In collections Multivariable Calculus
This example illustrates the concept of constrained optimization. Users can explore how to optimize a target function under given constraints using functions and geometric objects. The construction involves commands like CurveCartesian and Vector in GeoGebra. Suitable for high school mathematics education, particularly for learning calculus and optimization theory.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t), t, 0, 6.28) → S
  2. CurveCartesian(cos(t), sin(t), f(cos(t), sin(t)), t, 0, 6.28) → P
  3. CurveCartesian((sqrt(0.25) * cos(s)), (sqrt(0.25 / 2) * sin(s)), s, 0, 6.28) → d
  4. CurveCartesian((sqrt(0.5) * cos(s)), (sqrt(0.5 / 2) * sin(s)), s, 0, 6.28) → e
  5. CurveCartesian((sqrt(0.75) * cos(s)), (sqrt(0.75 / 2) * sin(s)), s, 0, 6.28) → g
  6. CurveCartesian(cos(s), (sqrt(1 / 2) * sin(s)), s, 0, 6.28) → a
  7. CurveCartesian((sqrt(1.25) * cos(s)), (sqrt(1.25 / 2) * sin(s)), s, 0, 6.28) → b
  8. CurveCartesian((sqrt(1.5) * cos(s)), (sqrt(1.5 / 2) * sin(s)), s, 0, 6.28) → h
  9. CurveCartesian((sqrt(1.75) * cos(s)), (sqrt(1.75 / 2) * sin(s)), s, 0, 6.28) → i
  10. CurveCartesian((sqrt(2) * cos(s)), sin(s), s, 0, 6.28) → j
  11. CurveCartesian((sqrt(2.25) * cos(s)), (sqrt(2.25 / 2) * sin(s)), s, 0, 6.28) → k
  12. CurveCartesian((sqrt(2.5) * cos(s)), (sqrt(2.5 / 2) * sin(s)), s, 0, 6.28) → l
  13. Vector(B, B + ((2 * cos(c)), (2 * sin(c)))) → u
  14. Vector(B, B + u / 4) → v
  15. Vector(((2 * cos(c)), (4 * sin(c)))) → w
  16. Vector(B, B + w / 4) → m