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How can we distribute 100 dollar on those 5 levels below to get the highest dollar amount.

Those 100 dollar needs to be 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 dollar on ALL 5 levels to get the highest dollar amount when we do a summation later for all 5 levels dollar amounts.

Example but this is not optimal:
1. 20% (20 dollar) : 0.20 * 20 dollar = 4 dollar
2. 30% (20 dollar) : 0.30 * 20 dollar = 6 dollar
3. 40% (20 dollar) : 0.40 * 20 dollar = 8 dollar
4. 25% (20 dollar) : 0.25 * 20 dollar = 5 dollar
5. 15% (20 dollar) : 0.15 * 20 dollar = 3 dollar

Andreas
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    Unless there are more conditions, put all of it into the highest percentage one every time. Try asking your actual question. Also, this has absolutely nothing to do with differential equations. – user3482749 Dec 04 '18 at 16:04
  • Thank you for changing to arithmetic. I am not sure that I follow you. Those 100d 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 100d on ALL 5 levels to get the highest procent when we do a summation later for all 5 levels procents. Example for level 1, if we put 10d it will be: 10d * 0.20 = 2d for that level etc – Andreas Dec 04 '18 at 16:11
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    Put 1 cent in each of the others, and all of the remainder in the highest-percentage one. – user3482749 Dec 04 '18 at 16:23
  • can we do $(0.01, 0.01, 99.96, 0.01, 0.01)$? – Vasily Mitch Dec 04 '18 at 16:23

1 Answers1

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I found a solution. We don't want to put 1 cent in the other ones. That would also be the optimal. We want to distribute the amount in an equal balanced manner as the percentages are like this:

We have a Total of 130%

0.1538 * 100 dollar = 15.38 dollar (20% of 130% = 15.38%)
0.2307 * 100 dollar = 23.07 dollar
0.3076 * 100 dollar = 30.76 dollar
0.1923 * 100 dollar = 19.23 dollar
0.1153 * 100 dollar = 11.53 dollar
Sum: 99.97 dollar (Just because of rounding wrong. This will be 100 dollar)

Andreas
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