IIT JEE 1982 Maths - MCQ Question 3
Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be traveled by all 200 students is to be as small as possible, then the school must be built at .
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1 solution
Choose some location between town A and town B. If we move one cm closer to town A then thats 1 5 0 cm less that students from town A must travel, and 5 0 more cm that students from town B must travel. So, 1 0 0 fewer total cm traveled by students for each cm closer to A you make it. Therefore, building it right on town A will minimize the total distance all the students need to travel.