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# Determine the coins to get hosting -- Minimize

GoldenEagle
So as a lot of you know, I like to try to come up with interesting things to talk about on here. Last time, I talked about using the FRIH\$ to model societies where the currency is only useable for a few things and found that in essence everyone is poor is that system. (See Economics board).

Today I was wondering about how many points I'd need to get to the my hosting. For simplicity I just rounded to state I have 300 coins : 50 coins to go.

First, we'll take the trivial solution : x^.6 = 50 ; x ~ 679 points.

Of course, the graph of y = x^.6 is not linearly increasing, so this method assumes the penalty of getting all of the points at once, which is not good (posting non-stop all day) and impossible given that we can only earn ~90 points a day.

So here's the question:

Of course I can stretch out the points over a few days (x1)^.06 + (x2)^.6 +.....(Xn)^.6 = 50

I'd like to minimize these values: # of Xn's (ie. days) & Values of each Xn

This is particularly complicated since earlier values of Xn impact future values.

Does anyone know of a method to solve this sort of problem? I am familiar with GAMs, but I'm not sure how to code the problem statement properly to get a solution.

I'd have to start with a succinct objective function: Minimize{ [PI(Xn*SUM((Xn/Xn),1...n), 1..n]}
ie a Geometric series with a summation in it.

Thoughts on my objective function?
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