To solve the optimization problem described, we will use the Gurobi Python API. The problem involves maximizing a complex objective function that includes terms related to the hours worked by Bill, Mary, George, and Dale, subject to numerous constraints involving organization score, productivity rating, paperwork competence rating, and computer competence rating.

Here's how we can set up the model:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables for hours worked by each person
Bill_hours = m.addVar(name="Bill_hours", lb=0)
Mary_hours = m.addVar(name="Mary_hours", lb=0)
George_hours = m.addVar(name="George_hours", lb=0)
Dale_hours = m.addVar(name="Dale_hours", lb=0)

# Define the objective function
m.setObjective(
    5 * Bill_hours**2 + 
    5 * Bill_hours * Mary_hours + 
    1 * Bill_hours * George_hours + 
    4 * Bill_hours * Dale_hours + 
    8 * Mary_hours**2 + 
    1 * Mary_hours * Dale_hours + 
    4 * George_hours**2 + 
    1 * George_hours * Dale_hours + 
    6 * Dale_hours**2 + 
    1 * Mary_hours + 
    1 * George_hours + 
    7 * Dale_hours,
    GRB.MAXIMIZE
)

# Constraints based on the provided information
m.addConstr(Bill_hours * 15 + Mary_hours * 5, GRB.GREATER_EQUAL, 50)
m.addConstr(Bill_hours * 15 + George_hours * 4, GRB.GREATER_EQUAL, 47)
m.addConstr(Mary_hours * 5 + George_hours * 4, GRB.GREATER_EQUAL, 19)
m.addConstr(Bill_hours * 1 + Mary_hours * 13, GRB.LESS_EQUAL, 232)
m.addConstr(Bill_hours * 1 + Dale_hours * 10, GRB.LESS_EQUAL, 252)
m.addConstr(Mary_hours * 12 + George_hours * 13, GRB.GREATER_EQUAL, 35)
m.addConstr(Bill_hours**2 * 7 + Mary_hours**2 * 12 + Dale_hours**2 * 11, GRB.GREATER_EQUAL, 40)

# Additional constraints
m.addConstr(Bill_hours * 15 + George_hours * 4 + Dale_hours * 9, GRB.GREATER_EQUAL, 38)
m.addConstr(Mary_hours * 5 + George_hours * 4 + Dale_hours * 9, GRB.GREATER_EQUAL, 38)
m.addConstr(Bill_hours * 15 + Mary_hours * 5 + Dale_hours * 9, GRB.LESS_EQUAL, 63)
m.addConstr(Bill_hours * 1 + George_hours * 14 + Dale_hours * 10, GRB.LESS_EQUAL, 261)

# Solve the model
m.optimize()

```python
```