(Originais Teachy 2024) - Question Hard of Mathematics

In the city of Geometropolis, the streets were planned in such a way that they always meet at perfect right angles, forming a true tangle of straight lines. A citizen, Mr. Mathematician, needs to move from point A, located at the intersection of Matriz Street with Even Numbers Street, to point B, located at the intersection of Fundamental Theorem Street with Parallel Street. He wants to find the shortest path, which would necessarily be a straight line. However, the streets, although all straight, have different paving materials for construction reasons, and the cost of traveling through each of them is different. Matriz Street is considered a special road and has zero cost, Even Numbers Street has a unit cost of 5 monetary units per meter traveled, Fundamental Theorem Street costs 10 monetary units per meter, and Parallel Street, due to its luxurious finish, costs 15 monetary units per meter. Considering that Mr. Mathematician must follow a route consisting of exactly two straight segments, in addition to the initial stretch where he is, and that he can freely choose which sequence of streets to take, how should he plan his route to minimize the total cost of the journey, knowing that the length of the streets is 100 meters between each intersection and that he needs to travel a total of 300 meters?