To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using mathematical notation.

Let's denote:
- $x_0$ as the hours worked by Jean,
- $x_1$ as the hours worked by Paul.

The objective function to minimize is: $9x_0 + 9x_1$

The constraints based on the given problem description are:
1. Work quality rating constraint: $7x_0 + 5x_1 \geq 29$
2. Combined work quality rating upper bound: $7x_0 + 5x_1 \leq 104$
3. Paperwork competence rating constraint: $7x_0 + 8x_1 \geq 40$
4. Combined paperwork competence rating upper bound: $7x_0 + 8x_1 \leq 55$
5. Additional linear constraint: $8x_0 - 6x_1 \geq 0$

Symbolic representation:
```json
{
    'sym_variables': [('x0', 'hours worked by Jean'), ('x1', 'hours worked by Paul')],
    'objective_function': '9*x0 + 9*x1',
    'constraints': [
        '7*x0 + 5*x1 >= 29',
        '7*x0 + 5*x1 <= 104',
        '7*x0 + 8*x1 >= 40',
        '7*x0 + 8*x1 <= 55',
        '8*x0 - 6*x1 >= 0'
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define the variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Jean")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Paul")

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

# Add constraints
m.addConstr(7*x0 + 5*x1 >= 29, "work_quality_rating_constraint")
m.addConstr(7*x0 + 5*x1 <= 104, "combined_work_quality_upper_bound")
m.addConstr(7*x0 + 8*x1 >= 40, "paperwork_competence_rating_constraint")
m.addConstr(7*x0 + 8*x1 <= 55, "combined_paperwork_competence_upper_bound")
m.addConstr(8*x0 - 6*x1 >= 0, "additional_linear_constraint")

# Optimize the model
m.optimize()

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