# Find average income from multiple sources with a time frame.

I'm trying to grasp the math behind a game but apparently I'm too illiterate for it.

You can have 10 territories each with 4 gold mines each with 10 levels. The time needed to reach that potential is 2 months. So over the course of 6 days you can progress to have 1 territory filled up with 4 mines level 10.

How can I calculate the total income i would have for 2 months?(considering i progressed that way)

I guess i need the average daily and multiply it by 60 but. I'm not sure if the average is based on 5 territories 2 mines level 5 or 5 territories 4 mines level 5. -Either way the process of how to do this is beyond my current knowledge.

Heh, I almost expired at figuring out which TAGS to put on this question. Apparently as a non English native speaker I don't even know the difference between algebra and calculus.

Extra info:

I start with 1 Territory with 0 mines. You can say i gain a mine level every 260 minutes and the income increases by the same amount at any level. I gain mines at that rate until i have the max 10 territory and 4 mines each level 10 each. You can suppose i get 100 per hour per mine level.

• You need to define what happens well enough to calculate the income each day. How many mines do you start with? How does its income increase with time? When do you start new mines? Once you define the question well enough, there are formulas like for the sum of an arithmetic progression that will probably help. Feb 12, 2015 at 15:59
• Is that good enough? Feb 13, 2015 at 8:48

The critical observation is that the production of any mine is proportional to its level. The total production is then proportional to the total of all the levels of all the mines, so we don't have to worry about how many mines you have and what levels, just that the total level increases from $0$ to $400$ with one step every $260$ minutes. We can measure time in time steps of $260$ minutes, so in the first time step you have no production, in the second step you have one unit of production, which is $100 \cdot \frac {260}{60}=\frac {1300}3=u$. In the second step you produce $2u$ and so on up to the $401$st step where you produce $400u$. Every step after that you produce $400u$. $60$ days is $60\cdot \frac {1440}{260}\approx 332.3$ time units. Your production in the first $332$ is $0+1+2+\dots +331=\frac 12\cdot 331 \cdot 332 = 54,946$ units. Your production in the last bit is $0.3*332 \approx 100$ units, so the total in two months is about $55,046$ units. To get the sum of the long list of numbers, you can see triangular numbers. If your production increased faster than linearly with level, you would want to raise the first mine to level $10$ before starting a second. You would do a similar analysis for a single mine, then use the time of raising a mine to level $10$ as the time step for a second one.