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3D Linear Programming Problem

3D Linear Programming Problem
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2020-06-04 22:12
Coordinate GeometrySolid GeometryOptimization
This is a 3D linear programming problem, demonstrating the basic concepts of linear programming through the construction of planes, intersections, and other geometric objects. It uses commands like Plane, IntersectPath, Intersect, and Polygon in GeoGebra. Suitable for high school mathematics education, particularly in coordinate geometry and linear programming courses.

GeoGebra Commands & Parameters

  1. Plane(A, B, C) → a
  2. IntersectPath(a, b) → f
  3. IntersectPath(a, d) → g
  4. IntersectPath(a, e) → h
  5. IntersectPath(c, d) → i
  6. IntersectPath(c, e) → j
  7. IntersectPath(c, b) → k
  8. IntersectPath(c, a) → l
  9. Intersect(xAxis, zAxis) → D
  10. Polygon(A, D, C) → t1, c_1, a_1, d_1
  11. Polygon(D, B, C) → t2, c_2, d_2, b_1
  12. Polygon(A, D, B) → t3, b_2, a_2, d_3
  13. Polygon(C, D, B) → t4, b_3, c_3, d_4

AI Drawing Prompt Reference

Create a 3D geometric figure for a linear programming problem. Start with a 3D coordinate system, choose three points on the positive x, y, and z axes, forming a tetrahedron. Construct three planes through pairs of these points, and add a fourth plane intersecting them, creating several intersection lines. Then connect the intersection points with polygons to form four triangular faces, resulting in a closed polyhedron that illustrates the feasible region and constraint planes in linear programming.
The prompt above was compiled from the original drawing commands and is for reference only.