Use dynamic programming to find N nonnegative numbers, say Subscript[x, 1],...,Subscript[x, N], to maximize \!\( \*UnderoverscriptBox[\(\[Product]\), \(i = 1\), \(N\)] \*SubscriptBox[\(x\), \(i\)]\) subject to the constraint \!\( \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(N\)] \*SubscriptBox[\(x\), \(i\)]\)=Overscript[x, _], where N is a positive integer and Overscript[x, _] is a given nonnegative number