If a,b and c are positive real numbers, such that (1+a)(1+b)(1+c) = 8 then the maximum value of a.b.c

Question

If
abcde=1 (where a,b,c,d and e are all positive real numbers)
then
what is the minimum value of a+b+c+d+e?

Answer 1

Cube root of 8 = 2
Therefore (1+a) = 2 = (1+b) = (1+c) {any other values of a, b & c that yields 8 as the answer will have at least 1 negative variable}
a = 1 = b = c
Therefore max of a×b×c = 1 in the domain of (1+a)(1+b)(1+c) = 8