Question

Two towns A and B are 60km apart. A school has to be built to serve 150
students of A, 50 students of town B. If the total distances to be travelled by
all the 200 students to be as small as possible, then where is the school to
be built?​

Answer 1

Explanation:

Let the school be at a distance x km from the town A.

Then the distance of school from town B=(60−x)km

Distance travelled by 150 students of town A=150x

Distance travelled by 50 students of town B=50(60−x)

So, total distance travelled by 200 students D=150x+3000−50x

D=f(x)=100x+3000

Clearly D is least when x=0

Hence, the school should be built at town A.

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