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Analytical solutions for some problems of optimum with applications in air traffic and economics are given. For air traffic minimal distances between commercial airplanes (flight corridors) are imposed considering various trajectories: straightlines, orthodromes and loxodromes. Some other applications are related to target functions submitted to linear or nonlinear restrictions. Although specialized numerical codes exist the analytical solutions are useful giving a more clear understanding, suggesting new ways of approach and providing fast tests for preconception.