Library: Difference between revisions
From Melvor Idle
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{{BuildingBox}} | {{BuildingBox}} | ||
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: Error creating thumbnail: File missing Level 35Error creating thumbnail: File missing 2,500
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| Base Cost:
8,200 Error creating thumbnail: File missing , 700 Error creating thumbnail: File missing , 450 Error creating thumbnail: File missing
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| Maximum Built: 100 |
| Provides: Error creating thumbnail: File missing +0.25,
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Biomes: Grasslands
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The Library is a Township building that increases
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Education. The percentage is applied to the current
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Educationamount, and is NOT applied to the maximum
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Education. For the maximum
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Educationwith the fewest buildings, the Template:BuildingIcon should only be built once 100 Template:BuildingIcon-type buildings have already been built. After that, the buildings should be built in a 1:1 ratio: e.g. 106 Template:BuildingIcon and 6 Template:BuildingIcon.
When more than 100 buildings are required, to calculate the optimal number of each building from a total
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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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| Melvor Idle version v1.3.1 (Released: 30th October 2024) |
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| Other: Error creating thumbnail: File missing Beginners Guide •  Guides • Error creating thumbnail: File missing Bank • Error creating thumbnail: File missing Combat • Error creating thumbnail: File missing Mastery • Error creating thumbnail: File missing Money Making • Error creating thumbnail: File missing Shop •  Easter Eggs •  Pets • Error creating thumbnail: File missing Golbin Raid • Error creating thumbnail: File missing Full Version •  Throne of the Herald •  Atlas of Discovery • Error creating thumbnail: File missing Into the Abyss
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| Reference Tables: Items, Equipment, Experience Table, Upgrading Items, Combat Areas, Slayer Areas, Dungeons, Strongholds, The Abyss, Monsters |
