## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul', 'hours worked by George', and 'hours worked by Jean', which can be represented as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $8.52x_0 + 1.56x_1 + 5.06x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $10x_0 \leq 103$
- $9x_0 \leq 141$
- $14x_0 \leq 109$
- $13x_0 \leq 106$
- $14x_1 \leq 103$
- $8x_1 \leq 141$
- $11x_1 \leq 109$
- $14x_1 \leq 106$
- $2x_2 \leq 103$
- $14x_2 \leq 141$
- $11x_2 \leq 109$
- $12x_2 \leq 106$
- $14x_1 + 2x_2 \geq 23$
- $10x_0 + 14x_1 \geq 17$
- $10x_0 + 14x_1 + 2x_2 \geq 17$
- $9x_0 + 14x_2 \geq 40$
- $9x_0 + 8x_1 \geq 16$
- $8x_1 + 14x_2 \geq 45$
- $9x_0 + 8x_1 + 14x_2 \geq 45$
- $14x_0 + 11x_2 \geq 29$
- $14x_0 + 11x_1 \geq 19$
- $14x_0 + 11x_1 + 11x_2 \geq 19$
- $14x_1 + 12x_2 \geq 33$
- $13x_0 + 14x_1 \geq 22$
- $13x_0 + 14x_1 + 12x_2 \geq 22$
- $7x_1 - 3x_2 \geq 0$
- $10x_0 + 14x_1 + 2x_2 \leq 65$
- $14x_0 + 11x_1 \leq 63$
- $14x_1 + 12x_2 \leq 69$
- $x_0 \in \mathbb{Z}$
- $x_1 \in \mathbb{Z}$
- $x_2 \in \mathbb{Z}$

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Paul'), 
        ('x1', 'hours worked by George'), 
        ('x2', 'hours worked by Jean')
    ], 
    'objective_function': '8.52*x0 + 1.56*x1 + 5.06*x2', 
    'constraints': [
        '10*x0 <= 103', '9*x0 <= 141', '14*x0 <= 109', '13*x0 <= 106',
        '14*x1 <= 103', '8*x1 <= 141', '11*x1 <= 109', '14*x1 <= 106',
        '2*x2 <= 103', '14*x2 <= 141', '11*x2 <= 109', '12*x2 <= 106',
        '14*x1 + 2*x2 >= 23', '10*x0 + 14*x1 >= 17', '10*x0 + 14*x1 + 2*x2 >= 17',
        '9*x0 + 14*x2 >= 40', '9*x0 + 8*x1 >= 16', '8*x1 + 14*x2 >= 45',
        '9*x0 + 8*x1 + 14*x2 >= 45', '14*x0 + 11*x2 >= 29', '14*x0 + 11*x1 >= 19',
        '14*x0 + 11*x1 + 11*x2 >= 19', '14*x1 + 12*x2 >= 33', '13*x0 + 14*x1 >= 22',
        '13*x0 + 14*x1 + 12*x2 >= 22', '7*x1 - 3*x2 >= 0', 
        '10*x0 + 14*x1 + 2*x2 <= 65', '14*x0 + 11*x1 <= 63', '14*x1 + 12*x2 <= 69',
        'x0 >= 0', 'x1 >= 0', 'x2 >= 0'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by Paul
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # hours worked by George
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # hours worked by Jean

    # Objective function
    model.setObjective(8.52 * x0 + 1.56 * x1 + 5.06 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * x0 <= 103)
    model.addConstr(9 * x0 <= 141)
    model.addConstr(14 * x0 <= 109)
    model.addConstr(13 * x0 <= 106)

    model.addConstr(14 * x1 <= 103)
    model.addConstr(8 * x1 <= 141)
    model.addConstr(11 * x1 <= 109)
    model.addConstr(14 * x1 <= 106)

    model.addConstr(2 * x2 <= 103)
    model.addConstr(14 * x2 <= 141)
    model.addConstr(11 * x2 <= 109)
    model.addConstr(12 * x2 <= 106)

    model.addConstr(14 * x1 + 2 * x2 >= 23)
    model.addConstr(10 * x0 + 14 * x1 >= 17)
    model.addConstr(10 * x0 + 14 * x1 + 2 * x2 >= 17)
    model.addConstr(9 * x0 + 14 * x2 >= 40)
    model.addConstr(9 * x0 + 8 * x1 >= 16)
    model.addConstr(8 * x1 + 14 * x2 >= 45)
    model.addConstr(9 * x0 + 8 * x1 + 14 * x2 >= 45)
    model.addConstr(14 * x0 + 11 * x2 >= 29)
    model.addConstr(14 * x0 + 11 * x1 >= 19)
    model.addConstr(14 * x0 + 11 * x1 + 11 * x2 >= 19)
    model.addConstr(14 * x1 + 12 * x2 >= 33)
    model.addConstr(13 * x0 + 14 * x1 >= 22)
    model.addConstr(13 * x0 + 14 * x1 + 12 * x2 >= 22)
    model.addConstr(7 * x1 - 3 * x2 >= 0)

    model.addConstr(10 * x0 + 14 * x1 + 2 * x2 <= 65)
    model.addConstr(14 * x0 + 11 * x1 <= 63)
    model.addConstr(14 * x1 + 12 * x2 <= 69)

    # Non-negativity constraints
    model.addConstr(x0 >= 0)
    model.addConstr(x1 >= 0)
    model.addConstr(x2 >= 0)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Hours worked by Paul: ", x0.varValue)
        print("Hours worked by George: ", x1.varValue)
        print("Hours worked by Jean: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```