## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Jean' and 'hours worked by Paul', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $9x_1 + 9x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $7x_1 + 5x_2 \geq 29$
- $7x_1 + 5x_2 \geq 29$ (redundant with the previous one)
- $7x_1 + 8x_2 \geq 40$
- $7x_1 + 8x_2 \geq 40$ (redundant with the previous one)
- $8x_1 - 6x_2 \geq 0$
- $7x_1 + 5x_2 \leq 104$
- $7x_1 + 8x_2 \leq 55$

## 4: Remove redundant constraints
After reviewing, we can see that there are redundant constraints. The simplified list of constraints is:
- $7x_1 + 5x_2 \geq 29$
- $7x_1 + 8x_2 \geq 40$
- $8x_1 - 6x_2 \geq 0$
- $7x_1 + 5x_2 \leq 104$
- $7x_1 + 8x_2 \leq 55$

## 5: Create the symbolic representation of the problem
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'hours worked by Jean'), ('x2', 'hours worked by Paul')],
'objective_function': '9*x1 + 9*x2',
'constraints': [
    '7*x1 + 5*x2 >= 29',
    '7*x1 + 8*x2 >= 40',
    '8*x1 - 6*x2 >= 0',
    '7*x1 + 5*x2 <= 104',
    '7*x1 + 8*x2 <= 55'
]
}
```

## 6: Write the Gurobi code to solve the optimization problem
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='hours_worked_by_Jean', lb=0)  # You can work fractional hours
    x2 = model.addVar(name='hours_worked_by_Paul', lb=0)  # You can work fractional hours

    # Define the objective function
    model.setObjective(9 * x1 + 9 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(7 * x1 + 5 * x2 >= 29, name='work_quality_constraint')
    model.addConstr(7 * x1 + 8 * x2 >= 40, name='paperwork_competence_constraint')
    model.addConstr(8 * x1 - 6 * x2 >= 0, name='jean_paul_hours_constraint')
    model.addConstr(7 * x1 + 5 * x2 <= 104, name='max_work_quality_constraint')
    model.addConstr(7 * x1 + 8 * x2 <= 55, name='max_paperwork_competence_constraint')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'Hours worked by Jean: {x1.varValue}')
        print(f'Hours worked by Paul: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```