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n parallel segments of different (?) lengths

Source: Portugal OPM 1997 p6

May 18, 2024
algebracombinatoricsinequalities

Problem Statement

nn parallel segments of lengths a1≤a2≤a3≤...≤ana_1 \le a_2 \le a_3 \le ... \le a_n were painted to mark an airport atrium. However, the architect decided that the nn segments should have equal length. If the cost per meter of extending the lines is equal to the cost of reducing them, how long should the lines be in order to minimize costs?
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