## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Laura', 'hours worked by Mary', and 'hours worked by Ringo', 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': 265, 'x0': 18, 'x1': 10, 'x2': 11}
- 'r1': {'description': 'paperwork competence rating', 'upper_bound': 311, 'x0': 29, 'x1': 16, 'x2': 28}
- 'r2': {'description': 'work quality rating', 'upper_bound': 316, 'x0': 7, 'x1': 23, 'x2': 18}

## 3: Define the objective function
The objective function to maximize is $4x_0 + 3x_1 + 6x_2$.

## 4: List all the constraints
1. $10x_1 + 11x_2 \geq 36$
2. $18x_0 + 10x_1 \geq 46$
3. $18x_0 + 10x_1 + 11x_2 \geq 51$
4. $23x_1 + 18x_2 \geq 66$
5. $7x_0 + 23x_1 \geq 76$
6. $7x_0 + 18x_2 \geq 79$
7. $18x_0 + 11x_2 \leq 135$
8. $18x_0 + 10x_1 \leq 258$
9. $18x_0 + 10x_1 + 11x_2 \leq 196$
10. $29x_0 + 28x_2 \leq 257$
11. $29x_0 + 16x_1 + 28x_2 \leq 257$
12. $7x_0 + 18x_2 \leq 122$
13. $23x_1 + 18x_2 \leq 235$
14. $7x_0 + 23x_1 \leq 270$
15. $7x_0 + 23x_1 + 18x_2 \leq 270$
16. $x_0$ is an integer.

## 5: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Laura'), 
        ('x1', 'hours worked by Mary'), 
        ('x2', 'hours worked by Ringo')
    ], 
    'objective_function': '4*x0 + 3*x1 + 6*x2', 
    'constraints': [
        '10*x1 + 11*x2 >= 36',
        '18*x0 + 10*x1 >= 46',
        '18*x0 + 10*x1 + 11*x2 >= 51',
        '23*x1 + 18*x2 >= 66',
        '7*x0 + 23*x1 >= 76',
        '7*x0 + 18*x2 >= 79',
        '18*x0 + 11*x2 <= 135',
        '18*x0 + 10*x1 <= 258',
        '18*x0 + 10*x1 + 11*x2 <= 196',
        '29*x0 + 28*x2 <= 257',
        '29*x0 + 16*x1 + 28*x2 <= 257',
        '7*x0 + 18*x2 <= 122',
        '23*x1 + 18*x2 <= 235',
        '7*x0 + 23*x1 <= 270',
        '7*x0 + 23*x1 + 18*x2 <= 270',
        'x0 == int(x0)'
    ]
}
```

## 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
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by Laura
    x1 = model.addVar(name="x1")  # hours worked by Mary
    x2 = model.addVar(name="x2")  # hours worked by Ringo

    # Define the objective function
    model.setObjective(4 * x0 + 3 * x1 + 6 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(10 * x1 + 11 * x2 >= 36)
    model.addConstr(18 * x0 + 10 * x1 >= 46)
    model.addConstr(18 * x0 + 10 * x1 + 11 * x2 >= 51)
    model.addConstr(23 * x1 + 18 * x2 >= 66)
    model.addConstr(7 * x0 + 23 * x1 >= 76)
    model.addConstr(7 * x0 + 18 * x2 >= 79)
    model.addConstr(18 * x0 + 11 * x2 <= 135)
    model.addConstr(18 * x0 + 10 * x1 <= 258)
    model.addConstr(18 * x0 + 10 * x1 + 11 * x2 <= 196)
    model.addConstr(29 * x0 + 28 * x2 <= 257)
    model.addConstr(29 * x0 + 16 * x1 + 28 * x2 <= 257)
    model.addConstr(7 * x0 + 18 * x2 <= 122)
    model.addConstr(23 * x1 + 18 * x2 <= 235)
    model.addConstr(7 * x0 + 23 * x1 <= 270)
    model.addConstr(7 * x0 + 23 * x1 + 18 * x2 <= 270)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Laura: ", x0.varValue)
        print("Hours worked by Mary: ", x1.varValue)
        print("Hours worked by Ringo: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```