Library: Difference between revisions
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The '''{{PAGENAME}}''' is a [[Township]] building that increases {{Icon|Education|type=township}} | The '''{{PAGENAME}}''' is a [[Township]] building that increases {{Icon|Education|type=township}}. The percentage is applied to the current {{Icon|Education|type=township}} amount, and is NOT applied to the maximum {{Icon|Education|type=township}}. For the maximum {{Icon|Education|type=township}} with the fewest buildings, the {{BuildingIcon|Library}} should only be built once 100 {{BuildingIcon|School}}-type buildings have already been built. After that, the buildings should be built in a 1:1 ratio: e.g. 106 {{BuildingIcon|Academy}} and 6 {{BuildingIcon|Library|nolink=true}}. | ||
<!-- | |||
Equation source/proof | |||
School = Number of School buildings | |||
Bonus = Education from 1 School building = 15, 35, 75 or 100 | |||
Library = Number of Library buildings | |||
M = Modifier from 1 Library building = 1 (+1% Education per Library building) | |||
Total = Total number of education buildings | |||
Education = Total education | |||
1) Total = School + Library | |||
2) Education = Bonus*School*(100+M*Library)/100 | |||
Put both equations together and simplify | |||
Education = Bonus*School*(100+M*(Total - School))/100 | |||
Education = Bonus*(100+M*Total)/100*School - M*Bonus/100*School^2 | |||
Take derivative of Education with respect to School | |||
The maximum education is when the derivative is = 0 | |||
dEducation/dSchool = Bonus*(100+M*Total)/100 - 2*M*Bonus/100*School | |||
0 = Bonus*(100+M*Total) - 2*M*Bonus/100*School | |||
2*M*Bonus/100*School = Bonus*(100+M*Total)/100 | |||
3) 2*M*School = 100+M*Total | |||
Since M = 1, this simplifies to | |||
School = (100+Total)/2 | |||
---------- | |||
Substituting 1) and 3) together | |||
2*M*School = 100+M*Total | |||
Total = (2*M*School - 100)/M = School + Library | |||
2*School - 100/M = School + Library | |||
4) School = Library + 100/M | |||
---------- | |||
To derive the number of School and Library buildings from a desired total education | |||
1) Total = School + Library | |||
2) Education = Bonus*School*(100+M*Library)/100 | |||
3) 2*M*School = 100+M*Total | |||
4) School = Library + 100/M | |||
Substituting 2) and 4) together | |||
Education = Bonus*School*(100+M*Library)/100 | |||
Education = Bonus*School*(100+M*(School - 100/M))/100 | |||
Education = Bonus*School*(100+M*School-100)/100 | |||
Education = Bonus*School*(M*School)/100 | |||
Education = Bonus*M*School^2/100 | |||
School = sqrt(100/Bonus/M * Education) | |||
Since M = 1, this simplifies to | |||
School = sqrt(100/Bonus * Education) | |||
--> | |||
When more than 100 buildings are required, to calculate the optimal number of each building from a total {{Icon|Education|type=township}}, the following equations can be used:<br> | |||
<math>\textrm{Bonus} = \textrm{Education per School-type building} = 15, 35, 75 \textrm{ or } 100</math><br> | |||
<math>\textrm{School building count} = \sqrt{\frac{100}{\textrm{Bonus}}\textrm{Education}}</math><br> | |||
<math>\textrm{Library count} = \textrm{School count} - 100</math> | |||
{{TownshipBuildingUpgrades}} | {{TownshipBuildingUpgrades}} | ||
{{TownshipBuildingNav}} | {{TownshipBuildingNav}} | ||
{{Menu}} | {{Menu}} |
Revision as of 03:29, 18 November 2022
This page was last updated for (v1.1.1). |
Library |
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Building ID: melvorF:Library |
Requirements: Level 35 2,500 |
Base Cost:
8,200 , 700 , 450 |
Maximum Built: 100 |
Provides: +0.25, |
Biomes: Grasslands |
The Library is a Township building that increases Education. The percentage is applied to the current Education amount, and is NOT applied to the maximum Education. For the maximum Education with the fewest buildings, the Library should only be built once 100 School-type buildings have already been built. After that, the buildings should be built in a 1:1 ratio: e.g. 106 Academy and 6 Library.
When more than 100 buildings are required, to calculate the optimal number of each building from a total Education, the following equations can be used:
[math]\displaystyle{ \textrm{Bonus} = \textrm{Education per School-type building} = 15, 35, 75 \textrm{ or } 100 }[/math]
[math]\displaystyle{ \textrm{School building count} = \sqrt{\frac{100}{\textrm{Bonus}}\textrm{Education}} }[/math]
[math]\displaystyle{ \textrm{Library count} = \textrm{School count} - 100 }[/math]
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