Optimization A: The "Factory" Protocol
Context: Braiding typically takes 6–8 hours. This duration is a high "friction" variable ($\epsilon$) in User Behavior.
Phase II: UB (The Fatigue Limit)
$$ \text{UB:}\ E(\text{pain} \mid t) > \text{Tolerance} $$
- Observation: Clients delay returning because the service duration ($t$) is physically painful.
- The Error: The "User Interface" (the chair) has a low retention rate due to time cost.
Phase III: SGD (Parallelization)
$$ \text{SGD:}\ \min(t) \Rightarrow \sum_{i=1}^{n} x_i $$
- The Optimization: Nadine changes the variable $x$ from a scalar (1 stylist) to a vector (2–3 stylists per head).
- The Descent: She minimizes $t$ from 6 hours to 2 hours.
Phase V: Economic Calculation (Throughput)
$$ \text{EC:}\ \int_{0}^{24h} (R \cdot 3)\,dt $$
- Result: By reducing service time by 66%, seat turnover triples.
- Reseed: The surplus capital funds the housing for the extra staff (Search result mentions buying homes for staff), locking them into the system.
Optimization B: The Authenticity Supply Chain
Context: Immigrant entrepreneurs (Importers) optimizing "Inventory" rather than "Time."
Phase II: UB (The Rejection of Substitutes)
$$ \text{UB:}\ E(\text{taste} \mid x_{local}) \approx \text{Fail} $$
- Observation: The Diaspora client rejects local spinach ($x_{local}$) as a substitute for Ndole.
- The Signal: The "Error" ($\epsilon$) is the sensory gap between "Here" and "Home."
Phase III: SGD (Supply Line Descent)
$$ \text{SGD:}\ \frac{d(\text{Authenticity})}{d(\text{Logistics})} $$
- The Optimization: The entrepreneur optimizes the supply chain to bridge the geographic distance ($d$).
- The Cost: High logistics cost ($C_L$), but it minimizes $\epsilon$ (the taste gap) to zero.
Phase IV: UI/UX (Sensory UI)
$$ \text{UX:}\ \text{Signal}(\text{Smell}) \to \text{Trust} $$
- The Interface: The smell of the shop.
- The Experience: It validates the user's identity. If the smell is wrong, the User Experience fails instantly.