## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Paul' and 'hours worked by Jean'. Let's denote 'hours worked by Paul' as $x_1$ and 'hours worked by Jean' as $x_2$. The objective function to minimize is $8.11x_1 + 8.33x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- Productivity rating constraint: $1.18x_1 + 3.74x_2 \geq 40$
- Work quality rating constraint: $6.04x_1 + 5.88x_2 \geq 89$
- Organization score constraint: $1.18x_1 + 6.64x_2 \geq 33$
- Linear constraint: $2x_1 - 3x_2 \geq 0$
- Upper bounds:
  - Productivity rating: $1.18x_1 + 3.74x_2 \leq 133$
  - Work quality rating: $6.04x_1 + 5.88x_2 \leq 195$
  - Organization score: $1.18x_1 + 6.64x_2 \leq 110$

## 3: Create the symbolic representation
The symbolic variables are:
- $x_1$ for 'hours worked by Paul'
- $x_2$ for 'hours worked by Jean'

The objective function is: $8.11x_1 + 8.33x_2$

The constraints are:
1. $1.18x_1 + 3.74x_2 \geq 40$
2. $6.04x_1 + 5.88x_2 \geq 89$
3. $1.18x_1 + 6.64x_2 \geq 33$
4. $2x_1 - 3x_2 \geq 0$
5. $1.18x_1 + 3.74x_2 \leq 133$
6. $6.04x_1 + 5.88x_2 \leq 195$
7. $1.18x_1 + 6.64x_2 \leq 110$

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="hours_worked_by_Paul", lb=0)  # Lower bound is 0, assuming hours cannot be negative
x2 = model.addVar(name="hours_worked_by_Jean", lb=0)  # Lower bound is 0, assuming hours cannot be negative

# Define the objective function
model.setObjective(8.11 * x1 + 8.33 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(1.18 * x1 + 3.74 * x2 >= 40)
model.addConstr(6.04 * x1 + 5.88 * x2 >= 89)
model.addConstr(1.18 * x1 + 6.64 * x2 >= 33)
model.addConstr(2 * x1 - 3 * x2 >= 0)
model.addConstr(1.18 * x1 + 3.74 * x2 <= 133)
model.addConstr(6.04 * x1 + 5.88 * x2 <= 195)
model.addConstr(1.18 * x1 + 6.64 * x2 <= 110)

# Optimize the model
model.optimize()

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

## 5: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Jean')],
    'objective_function': '8.11*x1 + 8.33*x2',
    'constraints': [
        '1.18*x1 + 3.74*x2 >= 40',
        '6.04*x1 + 5.88*x2 >= 89',
        '1.18*x1 + 6.64*x2 >= 33',
        '2*x1 - 3*x2 >= 0',
        '1.18*x1 + 3.74*x2 <= 133',
        '6.04*x1 + 5.88*x2 <= 195',
        '1.18*x1 + 6.64*x2 <= 110'
    ]
}
```