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Linear Programming and Polygon Construction

Linear Programming and Polygon Construction
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2019-11-27 00:42
PolygonCoordinate GeometryOptimizationGeometric Construction
In collections Pyramid Puzzles
This example dynamically demonstrates linear programming problems, visually showing how the optimal solution is determined within a polygonal region. It involves core mathematical concepts such as linear inequalities, feasible regions, optimal solutions, polygon construction, and coordinate geometry. GeoGebra commands like Polygon and Midpoint, along with objects A, B, C, D, are used to construct the graphics and locus. Suitable for high school and above learners to understand the integration of linear programming and analytical geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f_6, g_6, h, i, C, D
  2. Polygon(D, C, 4) → poly2, j, k, l, m, E, F
  3. Polygon(F, E, 4) → poly3, n, p, q, r, G, H
  4. Polygon(H, G, 4) → poly4, s, t, a_6, b_6, I, J
  5. Polygon(J, I, 4) → poly5, c_6, d_5, e_5, f_1, K, L
  6. Midpoint(A, D) → M
  7. Midpoint(D, F) → N
  8. Midpoint(F, H) → O
  9. Midpoint(H, J) → P
  10. Midpoint(J, L) → Q
  11. Polygon(M, N, 4) → poly6, g_1, h_1, i_1, j_1, R, S
  12. Polygon(R, N, 4) → poly7, k_1, l_1, m_1, n_1, T, U
  13. Polygon(U, O, 4) → poly8, p_1, q_1, r_1, s_1, V, W
  14. Polygon(W, P, 4) → poly9, t_1, a_1, b_1, c_1, Z, A_1
  15. Midpoint(S, R) → B_1
  16. Midpoint(R, U) → C_1
  17. Midpoint(U, W) → D_1
  18. Midpoint(W, A_1) → E_1
  19. Polygon(B_1, C_1, 4) → poly10, d_1, e_1, f_2, g_2, F_1, G_1
  20. Polygon(F_1, C_1, 4) → poly11, h_2, i_2, j_2, k_2, H_1, I_1
  21. Polygon(I_1, D_1, 4) → poly12, l_2, m_2, n_2, p_2, J_1, K_1
  22. Midpoint(G_1, F_1) → L_1
  23. Midpoint(F_1, I_1) → M_1
  24. Midpoint(I_1, K_1) → N_1
  25. Polygon(L_1, M_1, 4) → poly13, q_2, r_2, s_2, t_2, O_1, P_1
  26. Polygon(O_1, M_1, 4) → poly14, a_2, b_2, c_2, d_2, Q_1, R_1
  27. Midpoint(P_1, O_1) → S_1
  28. Midpoint(O_1, R_1) → T_1
  29. Polygon(S_1, T_1, 4) → poly15, e_2, f_3, g_3, h_3, U_1, V_1
  30. Polygon(L, K, 4) → poly16, i_3, j_3, k_3, l_3, W_1, Z_1
  31. Polygon(Z_1, W_1, 4) → poly17, m_3, n_3, p_3, q_3, A_2, B_2
  32. Midpoint(L, Z_1) → C_2
  33. Midpoint(Z_1, B_2) → D_2
  34. Polygon(A_1, Q, 4) → poly18, r_3, s_3, t_3, a_3, E_2, F_2
  35. Polygon(F_2, C_2, 4) → poly19, b_3, c_3, d_3, e_3, G_2, H_2
  36. Midpoint(A_1, F_2) → I_2
  37. Midpoint(F_2, H_2) → J_2
  38. Polygon(K_1, E_1, 4) → poly20, f_4, g_4, h_4, i_4, K_2, L_2
  39. Polygon(L_2, I_2, 4) → poly21, j_4, k_4, l_4, m_4, M_2, N_2
  40. Midpoint(K_1, L_2) → O_2
  41. Midpoint(L_2, N_2) → P_2
  42. Polygon(R_1, N_1, 4) → poly22, n_4, p_4, q_4, r_4, Q_2, R_2
  43. Polygon(R_2, O_2, 4) → poly23, s_4, t_4, a_4, b_4, S_2, T_2
  44. Midpoint(R_1, R_2) → U_2
  45. Midpoint(R_2, T_2) → V_2
  46. Polygon(U_1, T_1, 4) → poly24, c_4, d_4, e_4, f_5, W_2, Z_2
  47. Polygon(Z_2, U_2, 4) → poly25, g_5, h_5, i_5, j_5, A_3, B_3
  48. Midpoint(V_1, U_1) → C_3
  49. Midpoint(U_1, Z_2) → D_3
  50. Polygon(C_3, D_3, 4) → poly26, k_5, l_5, m_5, n_5, E_3, F_3
  51. Polygon(E_3, D_3, 4) → poly27, p_5, q_5, r_5, s_5, G_3, H_3
  52. Midpoint(F_3, E_3) → I_3
  53. Midpoint(E_3, H_3) → J_3
  54. Polygon(I_3, J_3, 4) → poly28, t_5, a_5, b_5, c_5, K_3, L_3