How Can You Maximize the Product of Integers Given a Fixed Sum?

[mhill]

we must obtain 'N' and a(i) i=1,2,3,....,N on condition that

the product $$a(1)a(2)a(3)...a(N)$$ is the highest possible

$$a(1)+a(2)+a(3)+...+a(N)=73$$

every a(i) is positive

here N (this is the hardest part) is not known and must be calculated

 

[CRGreathouse]

Well, since $3^{1/3}>2^{1/2}=4^{1/4}$, I'd suggest using as many 3s as will fit, making the rest a 2 or 4. In this case twenty three 3s and one 4 would seem to be the best. Now just check my work and make sure I didn't miss something silly.