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| {{V|1.1.1}} | | {{V|1.1.2}} |
| {{BuildingBox}} | | {{BuildingBox}} |
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| 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}}. | | The '''{{PAGENAME}}''' is a {{Skill|Township}} building that increases {{Icon|Education|type=township}}, which in turn increases resource production additively with other production bonuses. |
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| <!--
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| Equation source/proof
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| School = Number of School buildings
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| Bonus = Education from 1 School building = 15, 35, 75 or 100
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| Library = Number of Library buildings
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| M = Modifier from 1 Library building = 1 (+1% Education per Library building)
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| Total = Total number of education buildings
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| Education = Total education
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| 1) Total = School + Library
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| 2) Education = Bonus*School*(100+M*Library)/100
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| Put both equations together and simplify
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| Education = Bonus*School*(100+M*(Total - School))/100
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| Education = Bonus*(100+M*Total)/100*School - M*Bonus/100*School^2
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| Take derivative of Education with respect to School
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| The maximum education is when the derivative is = 0
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| dEducation/dSchool = Bonus*(100+M*Total)/100 - 2*M*Bonus/100*School
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| 0 = Bonus*(100+M*Total) - 2*M*Bonus/100*School
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| 2*M*Bonus/100*School = Bonus*(100+M*Total)/100
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| 3) 2*M*School = 100+M*Total
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| Since M = 1, this simplifies to
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| School = (100+Total)/2
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| ----------
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| Substituting 1) and 3) together
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| 2*M*School = 100+M*Total
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| Total = (2*M*School - 100)/M = School + Library
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| 2*School - 100/M = School + Library
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| 4) School = Library + 100/M
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| ----------
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| To derive the number of School and Library buildings from a desired total education
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| 1) Total = School + Library
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| 2) Education = Bonus*School*(100+M*Library)/100
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| 3) 2*M*School = 100+M*Total
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| 4) School = Library + 100/M
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| Substituting 2) and 4) together
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| Education = Bonus*School*(100+M*Library)/100
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| Education = Bonus*School*(100+M*(School - 100/M))/100
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| Education = Bonus*School*(100+M*School-100)/100
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| Education = Bonus*School*(M*School)/100
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| Education = Bonus*M*School^2/100
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| School = sqrt(100/Bonus/M * Education)
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| Since M = 1, this simplifies to
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| School = sqrt(100/Bonus * Education)
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| -->
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| 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>
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| <math>\textrm{Bonus} = \textrm{Education per School-type building} = 15, 35, 75 \textrm{ or } 100</math><br>
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| <math>\textrm{School building count} = \sqrt{\frac{100}{\textrm{Bonus}}\textrm{Education}}</math><br>
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| <math>\textrm{Library count} = \textrm{School count} - 100</math>
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| {{TownshipBuildingUpgrades}} | | {{TownshipBuildingUpgrades}} |
| {{TownshipBuildingNav}} | | {{TownshipBuildingNav}} |
| {{Menu}} | | {{Menu}} |
