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Oil Pipeline Optimization Problem

Oil Pipeline Optimization Problem
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2016-11-28 22:52
CalculusDerivativeOptimization
This example demonstrates the optimization problem of minimizing the cost of piping oil both underwater and on land using calculus. It involves core math concepts like derivative applications, optimization, straight lines, and similar triangles in coordinate geometry. Constructed with GeoGebra commands like Segment, Dilate, Polygon, etc., it is suitable for high school and above students learning real-world applications of calculus optimization.

GeoGebra Commands & Parameters

  1. Segment(P, B) → q
  2. Segment(W, P) → n
  3. Segment(A, B) → h
  4. Dilate(W, If[0 < d ≤ 1, 1 - d, 0], P) → A'
  5. Segment(W, A') → i
  6. Dilate(P, If[1 < d ≤ 2, 2 - d, 0], B) → D'
  7. Segment(P, D') → j
  8. Polygon(A, P, W) → poly1, w, a_1, p
  9. Textfield(b) → InputBox1
  10. Textfield(c) → InputBox2
  11. Segment(A, P) → k
  12. Textfield(e) → InputBox3
  13. Angle(P, A, W) → α
  14. Segment(W, A) → l_1
  15. Textfield(u) → InputBox4
  16. Textfield(l) → InputBox5
  17. Translate(A, (0, -2)) → A'_1
  18. Translate(B, (0, -2)) → B'
  19. Segment(A'_1, B') → r
  20. Segment(B', B) → s
  21. Segment(A'_1, A) → t