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

## Step 2: Convert the given attributes into a usable format
The given attributes are:
- 'r0': {'description': 'productivity rating', 'upper_bound': 39, 'x0': 3, 'x1': 10, 'x2': 6}
- 'r1': {'description': 'organization score', 'upper_bound': 58, 'x0': 8, 'x1': 13, 'x2': 5}

## 3: Define the objective function
The objective function to maximize is $3.77x_0 + 5.17x_1 + 8.77x_2$.

## 4: List all the constraints
1. $3x_0 + 10x_1 + 6x_2 \geq 11$
2. $13x_1 + 5x_2 \geq 10$
3. $8x_0 + 5x_2 \geq 18$
4. $8x_0 + 13x_1 \geq 14$
5. $3x_0 + 10x_1 \leq 14$
6. $3x_0 + 6x_2 \leq 30$
7. $3x_0 + 10x_1 + 6x_2 \leq 30$
8. $13x_1 + 5x_2 \leq 54$
9. $8x_0 + 13x_1 \leq 20$
10. $8x_0 + 5x_2 \leq 29$
11. $8x_0 + 13x_1 + 5x_2 \leq 38$
12. $x_0$ is an integer
13. $x_1$ is an integer
14. $x_2$ is an integer

## 5: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'hours worked by Bill'), ('x1', 'hours worked by George'), ('x2', 'hours worked by Jean')],
'objective_function': '3.77*x0 + 5.17*x1 + 8.77*x2',
'constraints': [
    '3*x0 + 10*x1 + 6*x2 >= 11',
    '13*x1 + 5*x2 >= 10',
    '8*x0 + 5*x2 >= 18',
    '8*x0 + 13*x1 >= 14',
    '3*x0 + 10*x1 <= 14',
    '3*x0 + 6*x2 <= 30',
    '3*x0 + 10*x1 + 6*x2 <= 30',
    '13*x1 + 5*x2 <= 54',
    '8*x0 + 13*x1 <= 20',
    '8*x0 + 5*x2 <= 29',
    '8*x0 + 13*x1 + 5*x2 <= 38',
    'x0 % 1 == 0',
    'x1 % 1 == 0',
    'x2 % 1 == 0'
]
}
```

## 6: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name='hours_worked_by_Bill', vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name='hours_worked_by_George', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hours_worked_by_Jean', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(3.77 * x0 + 5.17 * x1 + 8.77 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(3 * x0 + 10 * x1 + 6 * x2 >= 11)
    model.addConstr(13 * x1 + 5 * x2 >= 10)
    model.addConstr(8 * x0 + 5 * x2 >= 18)
    model.addConstr(8 * x0 + 13 * x1 >= 14)
    model.addConstr(3 * x0 + 10 * x1 <= 14)
    model.addConstr(3 * x0 + 6 * x2 <= 30)
    model.addConstr(3 * x0 + 10 * x1 + 6 * x2 <= 30)
    model.addConstr(13 * x1 + 5 * x2 <= 54)
    model.addConstr(8 * x0 + 13 * x1 <= 20)
    model.addConstr(8 * x0 + 5 * x2 <= 29)
    model.addConstr(8 * x0 + 13 * x1 + 5 * x2 <= 38)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'Hours worked by Bill: {x0.varValue}')
        print(f'Hours worked by George: {x1.varValue}')
        print(f'Hours worked by Jean: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```