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Optimization of a Box Without Top

Optimization of a Box Without Top
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2019-12-05 22:58
FunctionOptimizationGeometric Construction
This is a visualization tool for a classic optimization problem, demonstrating how to maximize the volume of a box by adjusting its dimensions. Key mathematical concepts include geometric construction, function graphing, and optimization. Using GeoGebra commands such as Polygon, Segment, and Point, users can intuitively understand the construction process of the optimization problem. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → q1, a, b, d, c_1
  2. Polygon(A, E, 4) → poly1, f, g, h, i, F, G
  3. Polygon(H, C, 4) → poly2, j, k, l, m, I, J
  4. Polygon(K, L, N, M) → q2, k_1, l_1, n, m_1
  5. Polygon(L, B, O, N) → q3, l_2, b_1, o, n_1
  6. Polygon(Q, P, 4) → poly3, p, q, r, s, R, S
  7. Polygon(R, T, D, S) → q4, r_1, t, d_1, s_1
  8. Segment(J, F) → e
  9. Segment(F, M) → f_1
  10. Segment(M, P) → g_1
  11. Segment(P, J) → h_1
  12. Segment(R, N) → i_1
  13. Polygon(Q, P, T, D) → q5, q_1, p_1, t_1, d_2
  14. Polygon(M, K, B, O) → q6, m_2, k_2, b_2, o_1
  15. Point(Circle[W, 8 - (2 * c)]) → A_1
  16. Segment(W, A_1) → j_1
  17. Rotate(A_1, 35°, W) → B_1
  18. Segment(W, U) → a_1
  19. Segment(U, V) → e_1
  20. Segment(V, Z) → f_2
  21. Segment(Z, W) → g_2
  22. Segment(W, B_1) → h_2
  23. Line(Z, h_2) → i_2
  24. Line(B_1, g_2) → j_2
  25. Line(V, h_2) → n_2
  26. Intersect(i_2, j_2) → C_1
  27. Line(C_1, f_2) → p_2
  28. Intersect(n_2, p_2) → D_1
  29. Segment(W, B_1) → q_2
  30. Segment(B_1, C_1) → r_2
  31. Segment(C_1, Z) → s_2
  32. Segment(V, D_1) → t_2
  33. Segment(D_1, C_1) → a_2