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Why are the Vertices Important in Linear Programming

Why are the Vertices Important in Linear Programming
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2017-12-30 10:48
TriangleCoordinate GeometryOptimization
This example uses coordinate geometry to explain why the method of linear programming actually works. It involves key concepts such as triangles, coordinates, fractions, and percentages. Using GeoGebra commands like Polygon, Line, Intersect, PointIn, Segment, and Dilate, a clear linear programming model is constructed. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a, b, c, d
  2. Line(A, A + (0, 0, 1)) → h
  3. Line(B, B + (0, 0, 1)) → i
  4. Line(C, C + (0, 0, 1)) → j
  5. Line(D, D + (0, 0, 1)) → k
  6. Intersect(h, g) → E
  7. Intersect(i, g) → F
  8. Intersect(j, g) → G
  9. Intersect(k, g) → H
  10. PointIn(q1) → I
  11. Line(I, I + (0, 0, 1)) → l
  12. Intersect(l, g) → J
  13. Polygon(E, F, G, H) → q2, e_1, f_1, g_1, h_1
  14. Segment(A, B) → m
  15. Segment(B, C) → n
  16. Segment(C, D) → p
  17. Segment(D, A) → q
  18. Segment(H, G) → r
  19. Segment(G, F) → s
  20. Segment(F, E) → t
  21. Segment(E, H) → i_1
  22. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], E) → A'
  23. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], F) → B'
  24. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], G) → C'
  25. Dilate(D, If[0 < o ≤ 1, 1 - o, 0], H) → D'
  26. Segment(B, B') → j_1
  27. Segment(C, C') → k_1
  28. Segment(D, D') → m_1
  29. Segment(A, A') → l_1
  30. Dilate(I, If[1.5 < o ≤ 2.5, 2.5 - o, 0], J) → I'
  31. Segment(I, I') → n_1
  32. Textfield(f) → InputBox2
  33. Textfield(e) → InputBox1

AI Drawing Prompt Reference

Draw a quadrilateral in a plane, with a slanted plane intersecting vertical lines through its vertices, creating a second quadrilateral. Connect corresponding vertices of the two quadrilaterals with segments to form a prism-like structure. Place a point inside the first quadrilateral, drop a vertical line to the slanted plane, and connect the intersection point back to the original point. Additionally, from each vertex of the first quadrilateral, draw a segment toward the corresponding vertex of the second quadrilateral, with length controlled by a parameter, to show a shrinking effect. This illustrates the geometric basis of linear programming.
The prompt above was compiled from the original drawing commands and is for reference only.