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In the present research paper an idea for optimizing the positioning of serving units in modern tourist resorts is proposed using some adapted applications of mathematics in economics. This material is a new step forward for both authors who have treated the topic in their publications in the past. The new idea is that the serving units are not fixed on line segments (e.g. streets) but are chosen from a given area or district (for example a triangle) or are selected from a number of previously given points. The lo...