How can we distribute 100$ to get the highest % (Equations)

Question

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

Answer 1

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)