Maximize parts of 271

Calculus Level 5

If 271 is written as the sum of positive real numbers so as to maximize the product of the summands, how many summands would be there?

As an example: 271 can be written as sum of 200,70 and 1. The product of the summands here is 14000. You are supposed to maximize this product. Remember that there is no restriction on the number of summands.

Question from Nick's Mathematical Puzzle.
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