To solve the optimization problem described, we will use Gurobi, a powerful optimization software. The problem involves maximizing an objective function that includes terms related to the hours worked by three individuals (George, Paul, and Laura) while satisfying several constraints related to their paperwork competence ratings.

Here's how we can translate this into a Gurobi model:

1. **Variables**: We have three variables representing the hours worked by George, Paul, and Laura.
2. **Objective Function**: Maximize \(1 \times (\text{hours worked by George}) \times (\text{hours worked by Paul}) + 9 \times (\text{hours worked by George}) \times (\text{hours worked by Laura}) + 1 \times (\text{hours worked by Paul}) \times (\text{hours worked by Laura}) + 2 \times (\text{total hours worked by Laura})^2 + 9 \times (\text{hours worked by George}) + 8 \times (\text{hours worked by Paul})\).
3. **Constraints**:
   - \(29 \times (\text{hours worked by George})\) is the paperwork competence rating for George.
   - \(23 \times (\text{hours worked by Paul})\) is the paperwork competence rating for Paul.
   - \(25 \times (\text{hours worked by Laura})\) is the paperwork competence rating for Laura.
   - The sum of the squared hours worked by Paul and Laura multiplied by their respective ratings should be less than or equal to 266.
   - The combined rating from George and Paul's hours should be less than or equal to 208.
   - The combined rating from George and Laura's hours should be no more than 106.
   - The sum of the squared hours worked by all three multiplied by their respective ratings should be at most 268.
   - The total hours worked by all three should have a combined rating of 268 or less.

Given these points, we can formulate the Gurobi model. Note that since the variables are continuous (can be fractional), we don't need to specify them as integers in the model.

```python
from gurobipy import *

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

# Variables representing hours worked by each person
george_hours = m.addVar(lb=0, name="George_Hours")
paul_hours = m.addVar(lb=0, name="Paul_Hours")
laura_hours = m.addVar(lb=0, name="Laura_Hours")

# Objective function: Maximize the given expression
m.setObjective(
    george_hours * paul_hours + 
    9 * george_hours * laura_hours + 
    paul_hours * laura_hours + 
    2 * (laura_hours ** 2) + 
    9 * george_hours + 
    8 * paul_hours, 
    GRB.MAXIMIZE
)

# Constraints
m.addConstr(29 * george_hours <= 284, name="George_Competence")
m.addConstr(23 * paul_hours <= 266 / (paul_hours ** 2 + laura_hours ** 2) * paul_hours ** 2, name="Paul_Competence") # Adjusted to reflect the problem statement correctly
m.addConstr(25 * laura_hours <= 284, name="Laura_Competence")
m.addConstr((23 * (paul_hours ** 2)) + (25 * (laura_hours ** 2)) <= 266, name="Paul_Laura_Squared_Rating")
m.addConstr((29 * george_hours) + (23 * paul_hours) <= 208, name="George_Paul_Combined_Rating")
m.addConstr((29 * george_hours) + (25 * laura_hours) <= 106, name="George_Laura_Combined_Rating")
m.addConstr((29 * (george_hours ** 2)) + (23 * (paul_hours ** 2)) + (25 * (laura_hours ** 2)) <= 268, name="All_Squared_Ratings")
m.addConstr((29 * george_hours) + (23 * paul_hours) + (25 * laura_hours) <= 268, name="Total_Combined_Rating")

# Optimize the model
m.optimize()

# Print results if an optimal solution is found
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"George Hours: {george_hours.x}")
    print(f"Paul Hours: {paul_hours.x}")
    print(f"Laura Hours: {laura_hours.x}")
else:
    print("No optimal solution found")
```