To tackle this problem, we first need to translate the given natural language description into a symbolic representation that can be used to formulate the optimization problem. The variables in question are the hours worked by Hank and Paul, which we'll denote as `x0` and `x1`, respectively.

Given:
- `x0`: Hours worked by Hank
- `x1`: Hours worked by Paul

Objective Function:
The objective is to maximize `2*x0 + 9*x1`.

Constraints:
1. Organization score constraint: `27.19*x0 + 23.57*x1 >= 167` and `27.19*x0 + 23.57*x1 <= 229`
2. Likelihood to quit index constraint: `17.72*x0 + 23.11*x1 >= 34` and `17.72*x0 + 23.11*x1 <= 99`
3. Work quality rating constraint: `22.33*x0 + 15.33*x1 >= 67` and `22.33*x0 + 15.33*x1 <= 92`
4. Additional constraint: `2*x0 - 10*x1 >= 0`

Symbolic Representation:
```json
{
    'sym_variables': [('x0', 'hours worked by Hank'), ('x1', 'hours worked by Paul')],
    'objective_function': '2*x0 + 9*x1',
    'constraints': [
        '27.19*x0 + 23.57*x1 >= 167',
        '27.19*x0 + 23.57*x1 <= 229',
        '17.72*x0 + 23.11*x1 >= 34',
        '17.72*x0 + 23.11*x1 <= 99',
        '22.33*x0 + 15.33*x1 >= 67',
        '22.33*x0 + 15.33*x1 <= 92',
        '2*x0 - 10*x1 >= 0'
    ]
}
```

To solve this optimization problem, we'll use the Gurobi solver in Python. Here's how you can formulate and solve the problem:

```python
from gurobipy import *

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

# Add variables to the model
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Paul")

# Set the objective function
m.setObjective(2*x0 + 9*x1, GRB.MAXIMIZE)

# Add constraints to the model
m.addConstr(27.19*x0 + 23.57*x1 >= 167, "organization_score_min")
m.addConstr(27.19*x0 + 23.57*x1 <= 229, "organization_score_max")
m.addConstr(17.72*x0 + 23.11*x1 >= 34, "quit_index_min")
m.addConstr(17.72*x0 + 23.11*x1 <= 99, "quit_index_max")
m.addConstr(22.33*x0 + 15.33*x1 >= 67, "work_quality_rating_min")
m.addConstr(22.33*x0 + 15.33*x1 <= 92, "work_quality_rating_max")
m.addConstr(2*x0 - 10*x1 >= 0, "additional_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Hank: {x0.X}")
    print(f"Hours worked by Paul: {x1.X}")
    print(f"Objective function value: {m.ObjVal}")
else:
    print("No optimal solution found.")
```