Library: Difference between revisions

Library (view source)

Revision as of 03:29, 18 November 2022

2,208 bytes added , 18 November 2022

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Gau Cho

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 {{BuildingBox}}
-The '''{{PAGENAME}}''' is a [[Township]] building that increases {{Icon|Education|type=township}} reduces the price of buildings. The percentage is applied to the current {{Icon|Education|type=township}} amount, and is NOT applied to the maximum {{Icon|Education|type=township}}. Therefore, for an optimal Town, the player's first 100 {{Icon|Education|type=township}}-boosting buildings should be {{BuildingIcon|School}}-type buildings, and only then the 101th and all subsequent buildings should be this building.
+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
+) Total = School + Library
+) 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
+= Bonus*(100+M*Total) - 2*M*Bonus/100*School
+*M*Bonus/100*School = Bonus*(100+M*Total)/100
+) 2*M*School = 100+M*Total
+Since M = 1, this simplifies to
+School = (100+Total)/2
+----------
+Substituting 1) and 3) together
+*M*School = 100+M*Total
+Total = (2*M*School - 100)/M = School + Library
+*School - 100/M = School + Library
+) School = Library + 100/M
+----------
+To derive the number of School and Library buildings from a desired total education
+) Total = School + Library
+) Education = Bonus*School*(100+M*Library)/100
+) 2*M*School = 100+M*Total
+) 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}}
 {{TownshipBuildingNav}}
 {{Menu}}