Algebra · Linear functions · Optimization · Weighted distances · Triangle inequality
The villages \(A\) and \(B\) are \(3\) kilometres apart. There are \(100\) pupils living in village \(A\) and \(50\) pupils living in village \(B\). At what distance from village \(A\) should a school be built so that the total distance walked by all the pupils in the course of one day is as small as possible?
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Serbian Municipal Competition 2003, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source