Metal Mine

In-Game Description
Metal is the primary resource used in the foundation of your Empire. At greater depths, the mines can produce more output of metal.You can use the available metal for use in the construction of buildings, ships, defense systems, and research. As the mines drill deeper, more energy is required for maximum production. As metal is the most abundant of all resources available, its value is considered to be the lowest of all resources for trading.

Requirements

 * Available from the start

Is Required for:


 * N/A

Costs by Level
$$ \text{Cost} = \text{Base Cost} \cdot 1.5^{\text{Metal Mine Level}- 1} $$

(Base Cost is 60 Metal and 15 Crystal)

Production
$$\text{Production} = 30A \cdot M \cdot 1.1^{M}$$

$$ A \equiv \text{Universe Acceleration Factor} $$

$$ M \equiv \text{Metal Mine Level} $$

Please keep in mind, that this is only the Metal produced by Metal Mines. There is also a base production that each planet puts out without any mine. This number can be seen under the resource settings and is equal to 30 times the acceleration factor. With that factored in, production will equal:

$$ \text{Production} = 30A \cdot M \cdot {1.1}^{M} $$

Additionally production could depend on Plasma Technology Level. e.g.

$$ \text{Production} = 30\left(1 + \frac{PT}{100}\right) \cdot A \cdot M \cdot {1.1}^{M} + 30A $$

$$ PT \equiv \text{Plasma Technology Level} $$

(Note that Plasma Technology does not affect the base resource generation rate)

Energy Consumption
$$ \text{Energy} = \left\lfloor 10 \cdot \text{Metal Mine Level}\cdot 1.1^{\text{Metal Mine Level}}\right\rfloor$$

Resource Stat Table

 * Notes :
 * 1) Information in this table is based solely on the formulas found on this page
 * 2) In the above figures reference should be made to 'game hours', particularly on servers with increased speed
 * 3) This does not count possible lack of energy
 * 4) All Numbers are rounded down except for "Energy Use", which is rounded up in order to maintain accuracy with the tested in-game values. Not all in-game values were tested 

Production and Profit vs Cost
$$ \text{Time (hours)}=\frac{3}{4\cdot\text{Metal Mine Level}}\cdot\left(\frac{15}{11}\right)^\text{Metal Mine Level} $$

The formula above gives the amount of time in which the total metal production reaches the cost of that level of the metal mine.



The graph above says that, for example, if you built metal mine mine level 12, it will take less than 5 hours to take back your metals which you used to built that level. Metal mine level 12 costs 5189 metal, and produces 1297 metals per hour. Indeed, it takes about 4 hours to take you metal back.



Example:

From the graph we observe that if you built metal mine level 30, it will take it 20 days to produce as much as metal you used to built that level.

Metal mine 30 costs 7670042 metals, and it produces 15704 metals per hour. That makes 7670042 / 15704 = 488.41 hours = 20.35 days to produce as much as metal you used to built metal mine level 30.

$$ \text{Time (hours)} = \frac{20}{\text{Metal Mine Level} + 10} \cdot {\left(\frac{15}{11}\right)}^{\text{Metal Mine Level} - 1} $$

The formula above gives after what hours the profit of upgrading metal mine adds up to catch the cost of upgrading. In other words, upgrading your metal mine will cause an increment in your metal production, if you integrate this increment over time, after some time this integration will be equal to the cost of the upgrading. This formula gives this time period.



The graph above says that, if you upgrade your metal mine from level 13 to level 14, it will take approximately two days to start harvesting your investment.

If we do the calculations with actual data, upgrading from level 13 to level 14 gives 1594 - 1346 = 248 metal/hour. Metal mine level 14 costs 11677 metal. So the time to start making profit is

$$ \frac{11677 \; \text{metal}}{1594 \; \frac{\text{metal}}{\text{hour}} - 1346 \; \frac{\text{metal}}{\text{hour}}} = 47.08 \; \text{hours}$$

$$\frac{20}{14 + 10} \cdot {\left(\frac{15}{11}\right)}^{14 - 1} = 46.98 \; \text{hours}$$



From the graph above, we observe that if one upgrades his metal mine from level 31 to level 32, he will start to make profit out of it after one year, for level 39 to level 40 it becomes 3000 days!

Note that, all these production and profit calculations are considered only on metal production. We assume that crystal and energy is free. If we were to consider crystal and energy issues, the formula would have been multi-variable, the graph would have been 4th dimensional. And also if we considered fusion reactor and solar satellites as energy source it would have been a total mess. So in order to keep things simple, it is only explained on metal production.

Note furthermore, that one should take into account the opportunity cost of the metal used. The opportunity cost   is the sacrifice related to the second best choice available to someone. In this case for example, however difficult to determine, one could consider expanding his or her fleet to increase income from raiding. If the expected additional income from raiding exceeds the increase of metal production, one should choose to expand his of her fleet instead.