Look for some kind of equation

jackpotcity

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Nov 28, 2018
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If you have 5 levels with different procents on each level like below.
We also have a TOTAL of 100$ that we must distribute on those 5 levels(we must use all 5 levels)




How can we calculate the optimal way to distribute the 100$ to get
the highest procent?
(I have about 30 levels so I am after a function to use)




Thank you!




1. 20%
2. 30%
3. 40%
4. 25%
5. 15%
 
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I probably mean what the highest summation in $ will be in the end, if I explain it like this:

Those 100$ needs to put distributed on ALL 5 levels. You can not only put in on level 3 which would be the optimal.
How can we do this to find out the perfect balance to distribute all 100$ on ALL 5 levels to get the highest $ amount when we do a summation later for all 5 levels $ amounts.

Example but this is not optimal:
1. 20% (20$) : 0.20 * 20$ = 4$
2. 30%
(20$) : 0.30 * 20$ = 6$
3. 40%
(20$) : 0.40 * 20$ = 8$
4. 25%
(20$) : 0.25 * 20$ = 5$
5. 15%
(20$) : 0.15 * 20$ = 3$
 
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If I understand you correctly the goal is to distribute the $100 prize among all participants according to their 'achievement', ideally using all of the money.

I would normalize the achievement percentages:
Add up all earned percentages: 20% + 30% ... + 15% = 130 "points"
Calculate prize percentages:
1. 20/130 = 0.15 = 15%. Prize: 0.15 * $100 = $15
2. 30/130
...
5. 15/130

The individual prizes will add up to $100, plus/minus rounding error.
 
Yes you are right. That was exactly what I was looking for. I think I just found the same solution too. Thank you!
We have a Total of 130%

0.1538 * 130% = 15.38$ (20% of 130% = 15.38%)
0.2307 * 130% = 23.07$
0.3076 * 130% = 30.76$
0.1923 * 130% = 19.23$
0.1153 * 130% = 11.53$
Sum: 99.97$ (It will be 100$ when rounding correctly)
 
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