Problem 1428. Find the optimal shape to bring the maximum product by a given perimeter
Find the optimal shape (with Nopt sides, where Nopt is at least 3) to bring the maximum product of the sides length, given a specified perimeter.
Example: Assuming perimeter equals to 7 (p=7) then the known optimal value is Nopt=3 (a triangle, so 3 sides). let mark L1,L2,L3 the triangle sides length (L1+L2+L3=7), thus the product is L1*L2*L3 and we want the product to be as large as possible for your chosen number of sides Nopt.
Don't assume the perimeter is an integer. The side lengths need not be integers, although it is possible they might be so. And of course, you need to decide if the optimum happens for an equilateral polygon, so with equal side lengths, or if some other set of side lengths that collectively sum to p might be a better choice.
Difficulty level on a scale 1 to 10: 8