CORPORATION: Update documentation (#1191)

src/Documentation/doc/advanced/corporation/industry-supply-chain.md

@@ -2,10 +2,10 @@
 
 ## Basic term
 
-Industry consumes input materials and produces output materials/products. Most industry produces either materials or products, some industries produce both of them.
+Industry consumes input materials and produces output materials/products. Most industries produce either materials or products, some industries produce both of them.
 
 - Material industries are simple to bootstrap. We use them as starting/support industries.
-- Product industries are hard to bootstrap, but they generate massive profit.
+- Product industries are hard to bootstrap, but they generate massive profits.
 
 Each industry has different values of "factor":
 
@@ -15,32 +15,34 @@ Each industry has different values of "factor":
   - With product industry: affect the output product's [markup and rating](./product.md).
 - `AdvertisingFactor`: affect the number of units that we can sell ([AdvertFactor](./optimal-selling-price-market-ta2.md)).
 
-"Endgame" is the very late phase after the division passes the exponential growth. In this phase, new product is only marginally better than old products, and the profit increases slowly. For example, endgame of Tobacco is when profit reaches ~1e98/s.
+"Support industry" is the industry that provides high-quality input materials for other industries.
+
+"Endgame" is the very late phase after the division passes the exponential growth. In this phase, the new product is only marginally better than the old products, and the profit increases slowly. For example, the endgame of Tobacco is when profit reaches ~1e98/s.
 
 ## Criterion
 
 In order to choose good industries for our supply chain, we must consider many criteria:
 
-- Good synergy between industries. Industries must be able to support each other with "Export" feature. After rework in 2.3, quality of input material becomes crucial, importing high-quality materials from other industries is mandatory.
-- Must have an easy to start material industry for early rounds. This industry must have good combinations of boost materials' coefficients and boost materials' sizes. This ensures high division product multiplier that is the most crucial factor in early rounds. In 4 boost materials, Real Estate (material, not industry) should be noticed because of its tiny size.
-- Support industry is the industry that provide high-quality input material for other industries. High `ScienceFactor` is a bonus for support industry because its output material's quality can be boosted without much investment in early rounds.
+- Good synergy between industries. Industries must be able to support each other with the "Export" feature. After the reworking in 2.3, the quality of input material becomes crucial, and importing high-quality materials from other industries is mandatory.
+- Must have an easy-to-start material industry for early rounds. This industry must have good combinations of boost materials' coefficients and boost materials' sizes. This ensures a high division product multiplier that is the most crucial factor in early rounds. In 4 boost materials, Real Estate (material, not industry) should be noticed because of its tiny size.
+- High `ScienceFactor` is a bonus for the support industry because its output material's quality can be boosted without much investment in early rounds.
 - Must have a highly profitable product industry for late phases.
-  - It's preferred to require material from starting industry rather than to expand into another support industry.
-  - High `ScienceFactor`. This is necessary for high product's rating.
-  - High `AdvertisingFactor`. This means our product's selling price can be boosted greatly by Wilson and Advert. This is the most important factor for endgame. `AdvertisingFactor` scales tremendously good when you reach high advert bonuses (Awareness and Popularity). These bonuses are capped at ~1.7977e308.
-- Any worthy industry must have at least 1 input material. Spring Water is the only industry that does not need any input material. It may look convenient at first glance, but it's trap for newbie. Having no input material means the quality/rating of output material/product will always be capped at square root of its maximum value.
+  - It's preferred to require material from the starting industry rather than to expand into another support industry.
+  - High `ScienceFactor`. This is necessary for a high product's rating.
+  - High `AdvertisingFactor`. This means our product's selling price can be boosted greatly by Wilson and Advert. This is the most important factor for the endgame. `AdvertisingFactor` scales tremendously well when you reach high advert bonuses (Awareness and Popularity). These bonuses are capped at ~1.7977e308.
+- Any worthy industry must have at least 1 input material. Spring Water is the only industry that does not need any input material. It may look convenient at first glance, but it's a trap for newbies. Having no input material means the quality/rating of the output material/product will always be capped at the square root of its maximum value.
 
 ## Agriculture + Chemical + Tobacco
 
-Agriculture is inarguably the best starting industry. Its `realEstateFactor` is highest among all industries (0.72), and real estate's size is tiny (0.005). It means we can stock up on huge number of real estates and increase division product multiplier to extremely high value in early rounds.
+Agriculture is inarguably the best starting industry. Its `realEstateFactor` is highest among all industries (0.72), and real estate's size is tiny (0.005). It means we can stock up on a huge number of real estate and increase the division product multiplier to an extremely high value in early rounds.
 
-Chemical is the best support industry if we choose Agriculture as starting industry. It has highest `ScienceFactor` among all material industries (0.75). As you can see in my round 2's strategy, I invest minimal budget to Chemical division and it can still adequately boost Agriculture (after waiting for some RP).
+Chemical is the best support industry if we choose Agriculture as the starting industry. It has the highest `ScienceFactor` among all material industries (0.75). As you can see in round 2's strategy, we only need to invest a minimal budget in the Chemical division and it can still adequately boost the Agriculture division (after waiting for some RP).
 
-Agriculture and Chemical have great synergy. Agriculture needs Chemicals, produces Plants. Chemical needs Plants, produces Chemicals.
+Agriculture and Chemical have great synergy. Agriculture needs `Chemicals` from Chemical and produces `Plants`. Chemical needs `Plants` from Agriculture and produces `Chemicals`.
 
 Tobacco is an excellent product industry:
 
-- It requires only Plants, and Plants come from Agriculture. Therefore, quality of input material is not a problem with this industry if we choose Agriculture as starting industry.
+- It requires only Plants, and Plants come from Agriculture. Therefore, the quality of input material is not a problem with this industry if we choose Agriculture as the starting industry.
 - High `ScienceFactor` (0.75), only below Pharmaceutical.
 - High `AdvertisingFactor` (0.2), only below Restaurant and Real Estate.
 
@@ -48,16 +50,16 @@ Tobacco is an excellent product industry:
 
 All other product industries always have some kind of flaws in them and not be as versatile as Tobacco. For example:
 
-- Pharmaceutical has highest `ScienceFactor` (0.8) but low `AdvertisingFactor` (0.16).
-  - Its products are potentially better than Tobacco's ones. This sounds good in theory, but not in practice. Pharmaceutical requires Chemicals. Chemicals can only be produced by Chemical industry, and that industry has bad production capability. The early products' effective rating will be low because the Chemical division cannot produce enough high-quality material units. In the end, the offers of round 3 and 4 are much lower than Tobacco's ones.
-  - It is worse than Tobacco in endgame.
-- Healthcare has same `ScienceFactor` as Tobacco's one (0.75) but lowest `AdvertisingFactor` (0.11).
-  - It requires 4 input materials instead of 1 or 2. Those materials include Robots with coefficient of 10 (highest value of all industries), and size of Robots is biggest among boost materials. This means the required materials take up huge space in warehouse.
-  - This industry is the worst one in endgame because of its extremely low `AdvertisingFactor`.
-- Restaurant has highest `AdvertisingFactor` (0.25) but very low `ScienceFactor` (0.12).
+- Pharmaceutical has the highest `ScienceFactor` (0.8) but a low `AdvertisingFactor` (0.16).
+  - Its products are potentially better than Tobacco's ones. This sounds good in theory, but not in practice. Pharmaceutical requires Chemicals. Chemicals can only be produced by the Chemical industry, and that industry has bad production capability. The early products' effective rating will be low because the Chemical division cannot produce enough high-quality material units. In the end, the offers of round 3 and round 4 are much lower than Tobacco's ones.
+  - It is worse than Tobacco in the endgame.
+- Healthcare has the same `ScienceFactor` as Tobacco (0.75) but the lowest `AdvertisingFactor` (0.11).
+  - It requires 4 input materials instead of 1 or 2. Those materials include Robots with a coefficient of 10 (the highest value of all industries), and the size of Robots is the biggest among boost materials. This means the required materials take up huge space in the warehouse.
+  - This industry is the worst one in the endgame due to its extremely low `AdvertisingFactor`.
+- Restaurant has the highest `AdvertisingFactor` (0.25) but very low `ScienceFactor` (0.12).
   - Its products are significantly worse than Tobacco's ones. It takes too long to hit the exponential growth (due to worse products) and surpass Tobacco in profit.
-  - It's fine to expand into this industry after Tobacco to have better endgame.
-- Real Estate has same `AdvertisingFactor` as Restaurant's one but lowest `ScienceFactor` (0.05). It requires 4 input materials instead of 1 or 2. This industry has same potential and problem like Restaurant with its high `AdvertisingFactor` and low `ScienceFactor`. The only difference is that its `ScienceFactor` is even lower than Restaurant's one.
+  - It's fine to expand into this industry after Tobacco to have a better endgame.
+- Real Estate has the same `AdvertisingFactor` as Restaurant but the lowest `ScienceFactor` (0.05). It requires 4 input materials instead of 1 or 2. This industry has the same potential and problem as Restaurant with its high `AdvertisingFactor` and low `ScienceFactor`. The only difference is that its `ScienceFactor` is even lower than the Restaurant's one.
 
 ## Conclusion
 

src/Documentation/doc/advanced/corporation/office.md

@@ -37,11 +37,19 @@ $$Salary = 3\ast TotalEmployees\ast\left(AvgIntelligence+AvgCharisma+AvgCreativi
 
 Upgrade cost:
 
-$$UpgradeCost = BasePrice\ast{1.09}^{\frac{CurrentSize}{3}}$$
+$$UpgradeCost = BasePrice\ast\left( \frac{\sqrt[3]{1.09} - 1}{0.09} \right)\ast{1.09}^{\frac{CurrentSize}{3}}$$
 
 Upgrade cost from size 3 to size n:
 
-$$UpgradeCost_{From\ 3\ to\ n} = \sum_{k = 1}^{\frac{n}{3} - 1}{BasePrice\ast 1.09^k}$$
+$$UpgradeCost_{From\ 3\ to\ n} = \sum_{k = 3}^{n - 1}{BasePrice\ast\left( \frac{\sqrt[3]{1.09} - 1}{0.09} \right)\ast{1.09}^{\frac{k}{3}}}$$
+
+≡
+
+$$UpgradeCost_{From\ 3\ to\ n} = \sum_{k = 3}^{n - 1}{BasePrice\ast\left( \frac{\sqrt[3]{1.09} - 1}{0.09} \right)\ast\left( \sqrt[3]{1.09} \right)^{k}}$$
+
+≡
+
+$$UpgradeCost_{From\ 3\ to\ n} = BasePrice\ast\left( \frac{\sqrt[3]{1.09} - 1}{0.09} \right)\ast\left( \frac{\left( \sqrt[3]{1.09} \right)^{n} - 1.09}{\sqrt[3]{1.09} - 1} \right)$$
 
 ≡
 
@@ -53,7 +61,7 @@ $$UpgradeCost_{From\ a\ to\ b} = BasePrice\ast\left( \frac{{1.09}^{\frac{b}{3}}
 
 Maximum size with a given `MaxCost`:
 
-$$MaxUpgradeLevel = 3\ast\log_{1.09}\left( MaxCost\ast\frac{0.09}{BasePrice} + {1.09}^{\frac{CurrentSize}{3}} \right)$$
+$$MaxSize = 3\ast\log_{1.09}\left( MaxCost\ast\frac{0.09}{BasePrice} + {1.09}^{\frac{CurrentSize}{3}} \right)$$
 
 ## Energy and morale
 

src/Documentation/doc/advanced/corporation/product.md

@@ -23,7 +23,7 @@ The product's markup and rating are based on:
 - `ResearchFactor`. It is the industry's `scienceFactor`.
 - Design investment and advertising investment. Game UI shows them as "Design investment" and "Marketing investment". These two investments are not too important because their exponents in the formulas are very low. It's fine to use only 1% of current funds for them.
 
-Office's upgrade and employee stats' upgrades are very important for products because they increase employee production. High employee production means high CreationJobFactors and RP. Those upgrades and products create a powerful loop: More upgrades → Better product → Higher profit → More upgrades.
+Office's upgrade and employee stats' upgrades are very important for products because they increase employee production. High employee production means high `CreationJobFactors` and RP. Those upgrades and products create a powerful loop: More upgrades → Better product → Higher profit → More upgrades.
 
 Office setup is important to efficiently develop new products. Check this [section](./general-advice.md) for advice on how to set up the office.
 
@@ -155,7 +155,7 @@ $$Demand = \begin{cases}Min(100,AdvertInvestMult\ast(100\ast(Popularity/Awarenes
 $$Competition = Random(0,70)$$
 
 - Product's size:
-  - It's product.size.
+  - It's `product.size`.
   - Formula:
 
 $$ProductSize = \sum_{i = 1}^{NumberOfInputMaterials}{{InputMaterialSize}_i\ast{InputMaterialCoefficient}_i}$$