# what problem is this? [closed]

I have this instance:

Let's say I have two (could be more) friends, one weighing 200 pounds and another weighing 100 pounds; I won a box with 30 chocolates in a contest and I want to divide among these friends aiming at both having optimal satisfaction, measured by (chocolate)/(body weigh) ratio.

So far the problem is trivial, i give 20 chocolates to the heavier friend and 10 to the other; resulting in a chocolate/mass ratio of 1/10 for each.

But now let's assume they each had some chocolates beforehand, 3 for my thinner friend and 5 for the heavier one.

Now the problem gets complicated.

I have another instance with some 10 "friends" and the numbers are way larger. For this example I assumed the 30 chocolates were indivisible, but could also be divisible.

My question: what is this problem called? Are there any simple algorithms for it?

• Please use a more informative title. Also please check tour and help center for the scope of cstheory. – Kaveh Sep 18 '13 at 2:23

If you allow chocolate division, you simply have a linear system of equations in $\mathbb{Q}$.