Library: Difference between revisions

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(Update for v1.1.2)
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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.
 
<!--
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>


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Revision as of 12:22, 16 May 2023

This page was last updated for (v1.1.2).


Library
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Building ID: melvorF:Library
Requirements:
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Level 35

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 2,500
Base Cost: 8,200
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, 700
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, 450
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Maximum Built:
100
Provides:
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 +0.25,
Biomes:
Grasslands

The Library is a

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Township

building that increases

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Education

, which in turn increases resource production additively with other production bonuses.



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Township
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Population
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Basic Shelter
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Wooden Hut
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House
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Cottage
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Large Cottage
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Manor
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Estate
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Storage
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Storehouse
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Warehouse
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Repository
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Large Repository
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Happiness
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Tavern
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Gardens
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Education
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School
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Large School
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Academy
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Large Academy
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Library
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Worship
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Chapel
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Statue of Worship
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Trading
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Trading Post
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Prats Hats
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Malcs Cats
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Cool Rocks
Food
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Farmland
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Plantation
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Mill
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Farming Estate
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Fishermans Dock
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Fishermans Pier
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Fishermans Port
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Fishermans Estate
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Orchard
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Market
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Wood
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Woodcutters Camp
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Logging Camp
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Forestry Camp
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Forestry Estate
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Planks
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Carpenters Workshop
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Carpenters Factory
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Carpenters Foundry
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Carpenters Estate
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Stone
,
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Ore
& Coal
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Miners Pit
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Miners Field
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Miners Quarry
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Miners Estate
Bar
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Blacksmiths Smithy
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Blacksmiths Workshop
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Blacksmiths Forge
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Blacksmiths Estate
Rune Essence
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Magic Emporium
Herbs
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Gatherers Hut
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Gatherers Lodge
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Gatherers Villa
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Gatherers Estate
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Potions
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Herbalist
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Infirmary
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Healing Centre
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Hospital
Leather
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Hunters Cabin
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Hunters Lodge
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Hunters Villa
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Hunters Estate
Clothing
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Tailor
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Clothier
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Outfitter
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Clothiers Estate
Other
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Cemetery
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Town Hall
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Lemvor Lemon Stall
Gateway
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Abyssal Gateway
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Fortification
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Wooden Walls
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Stone Walls
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Obsidian Walls
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Empowered Altar
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Arcane Altar
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Ethereal Altar
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Enchanted Tower
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Soul Storage
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Sanctuary
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Divine Sanctuary
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Ethereal Sanctuary
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Void Sanctuary
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Armour & Weaponry
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Armourer I
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Armourer II
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Armourer III
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Armourer I
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Armourer IV
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Weaponsmith I
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Weaponsmith II
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Weaponsmith III
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Weaponsmith IV
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Abyssal Stone
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Abyssal Harvester I
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Abyssal Harvester II
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Abyssal Harvester III
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Reinforced Planks
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Reinforced Carpenter I
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Reinforced Carpenter II
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Reinforced Carpenter III
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Obsidian
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Obsidian Mines
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Obsidian Quarry
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Obsidian Blaster
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Runestone
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Runestone Crafter
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Runestone Combiner
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Runestone Merger
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Voidfire Ash
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Fire Pit
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Bonfire
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Voidfire Beacon
Abyssal Buffs
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Abyssal Enhancer
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Abyssal Research Lab
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Slayer Research Lab
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Abyssal Combat Lab