To solve the optimization problem described, we need to formulate it as a linear programming (LP) problem and then use Gurobi, a powerful solver for mathematical optimization problems, to find the solution. The variables in our problem are 'hours worked by Jean' (let's denote this as `x0`) and 'hours worked by Paul' (`x1`). We aim to minimize the objective function `9*x0 + 9*x1`.

Given constraints:
- The total combined work quality rating from hours worked by Jean and Paul should be at least 29.
- The total combined paperwork competence rating from hours worked by Jean and Paul should be at least 40.
- `8*x0 - 6*x1 >= 0`.
- The total combined work quality rating should not exceed 104.
- The total combined paperwork competence rating should not exceed 55.

Formulating these into mathematical expressions:
- Work quality constraint: `7*x0 + 5*x1 >= 29`
- Paperwork competence constraint: `7*x0 + 8*x1 >= 40`
- Linear constraint: `8*x0 - 6*x1 >= 0`
- Upper bound work quality constraint: `7*x0 + 5*x1 <= 104`
- Upper bound paperwork competence constraint: `7*x0 + 8*x1 <= 55`

Here's how we can represent this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(lb=0, name="hours_worked_by_Jean")  # Hours worked by Jean
x1 = m.addVar(lb=0, name="hours_worked_by_Paul")  # Hours worked by Paul

# Objective function: Minimize 9*x0 + 9*x1
m.setObjective(9*x0 + 9*x1, GRB.MINIMIZE)

# Constraints
# Work quality constraint
m.addConstr(7*x0 + 5*x1 >= 29, name="work_quality_constraint")

# Paperwork competence constraint
m.addConstr(7*x0 + 8*x1 >= 40, name="paperwork_competence_constraint")

# Linear constraint
m.addConstr(8*x0 - 6*x1 >= 0, name="linear_constraint")

# Upper bound work quality constraint
m.addConstr(7*x0 + 5*x1 <= 104, name="upper_bound_work_quality")

# Upper bound paperwork competence constraint
m.addConstr(7*x0 + 8*x1 <= 55, name="upper_bound_paperwork_competence")

# Optimize the model
m.optimize()

# Print solution
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")
```