# How to split $100$% to various components with different priorities?

For the following scenario :

$E=100$ (energy available = $100$%)

Components = $N$ (can be $1,2,3,\dots,\infty$)

Now I want to split $E=100$ for each component, however, components are prioritised :

Example, component $1$ has first priority, component $2$ has second highest priority, and the rest have low priorities.

Application : If $E=100$

• $C_1=1$ (component $1$ has priority 1 )
• $C_2=2$
• $C_3=3,C_4=3,C_5=3$

Then $C_1$ must get the maximum value of $E$, while $C_2$ gets the second highest value ... $C_{345}$ must get the same equal lowest value of $E$

What mathematical model achieves this ?

Splitting $100/5$ will only give me equal values for all components, but im not sure how to achieve this with priorities.

• This is some kind of optimization problem, yet you do not specify how to compare two distributions. – Alexei Averchenko Nov 6 '12 at 16:17
• @AlexeiAverchenko to be honest, I have no idea what to call this .. I am not familiar with the mathematical terms or titles. I just thought they have something to do with models and division ... Can you elaborate what you mean by specifying how to compare two distributions ? -- Also, did you mark my question down ? – NLed Nov 6 '12 at 16:19
• Suppose you have two distributions $(a_1, a_2, \ldots, a_n)$ and $(b_1, b_2, \ldots, b_n)$. How do you determine which one is better for you purposes? – Alexei Averchenko Nov 6 '12 at 16:21
• Each distribution will be given a priority. The distribution with highest priority gets most of the weighting. – NLed Nov 6 '12 at 16:30
• No-no-no, suppose two hypothetical situations: in one you've given $a_1$ to the first guy, $a_2$ to the second guy etc., in the other you've given $b_1$ to the first guy, $b_2$ to the second guy etc. How do you determine which allocation/split/solution/how-do-you-call-it is better than the other? – Alexei Averchenko Nov 6 '12 at 17:08