perplexus.info :: Just Math : Optimal result

Optimal result (Posted on 2018-06-04)

A stick of length L is broken into n equal parts.

What is the maximal product of their lengths?

No Solution Yet Submitted by Ady TZIDON

Rating: 2.0000 (1 votes)

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| Comment 7 of 11 |

Just may have just been solved, but here what I got anyway....

To get max [ (L/n)^n ] = max [L^n / n^n], get the max of

the ln of this:

(n ln L - n ln n)

d/dn (n ln L = n ln n) = 0

ln L - ( n 1/n + ln n) = 0

ln n = ln L -1

n = exp (ln L - 1)

Posted by Steven Lord on 2018-06-05 14:15:40

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