SOLUTION: Please help me with this! My math problem asks to add any amount of positive numbers with the sum of 25. It then asks the product of those numbers, and the goal is to have the larg

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Please help me with this! My math problem asks to add any amount of positive numbers with the sum of 25. It then asks the product of those numbers, and the goal is to have the larg      Log On


   

Question 1134112: Please help me with this! My math problem asks to add any amount of positive numbers with the sum of 25. It then asks the product of those numbers, and the goal is to have the largest possible product. The highest product I found so far is 8,748, and the numbers I used are 4+3+3+3+3+3+3+3 (these numbers add up to 25 but multiply to 8,748). I was told there was a larger possible product. I have tried other sets but nothing I have found so far is higher.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The key here is "positive numbers" does not mean positive integers. Once you
accept the number just needs to be real, your first thought should be 'e':


+25%2Fe+ is approx 9.19699

+e%5E9.19699+ is approx +highlight%289867.344%29+

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.

To get familiar with the relevant Mathematical background behind this problem, look into the link

https://www.quora.com/What-is-the-maximum-product-of-any-number-of-positive-integers-that-have-a-sum-of-12-What-about-100-What-if-you-arent-limited-to-integers

https://www.quora.com/What-is-the-maximum-product-of-any-number-of-positive-integers-that-have-a-sum-of-12-What-about-100-What-if-you-arent-limited-to-integers