## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Ringo', 'hours worked by Hank', and 'hours worked by Laura', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the given attributes into a usable format
The computer competence ratings are given as: $r_0$ with $x_0 = 7$, $x_1 = 14$, and $x_2 = 10$. This implies that the computer competence rating for Ringo, Hank, and Laura are 7, 14, and 10 respectively.

## 3: Formulate the objective function
The objective function to minimize is $4.1x_1 + 6.3x_2 + 7.72x_3$.

## 4: Define the constraints
1. $7x_1 \geq 7$ is not needed as $x_1$'s coefficient is fixed at 7.
2. $14x_2 \geq 14$ is not needed for the same reason.
3. $10x_3 \geq 10$ is also not needed.
4. $7x_1 + 10x_3 \geq 19$.
5. $7x_1 + 14x_2 \geq 20$.
6. $7x_1 + 14x_2 + 10x_3 \geq 20$.
7. $6x_2 - 4x_3 \geq 0$.
8. $7x_1 + 14x_2 \leq 52$.
9. $x_1$ and $x_2$ can be fractional, but $x_3$ must be an integer.

## 5: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Hank'), ('x3', 'hours worked by Laura')],
    'objective_function': '4.1*x1 + 6.3*x2 + 7.72*x3',
    'constraints': [
        '7*x1 + 10*x3 >= 19',
        '7*x1 + 14*x2 >= 20',
        '7*x1 + 14*x2 + 10*x3 >= 20',
        '6*x2 - 4*x3 >= 0',
        '7*x1 + 14*x2 <= 52',
        'x3 >= 0 and x3 == Integer' # Ensuring x3 is a non-negative integer
    ]
}
```

## 6: Gurobi Code
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Ringo", lb=0)  # Ringo
    x2 = model.addVar(name="hours_worked_by_Hank", lb=0)  # Hank
    x3 = model.addVar(name="hours_worked_by_Laura", lb=0, vtype=gurobi.GRB.INTEGER)  # Laura

    # Objective function
    model.setObjective(4.1 * x1 + 6.3 * x2 + 7.72 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(7 * x1 + 10 * x3 >= 19)
    model.addConstr(7 * x1 + 14 * x2 >= 20)
    model.addConstr(7 * x1 + 14 * x2 + 10 * x3 >= 20)
    model.addConstr(6 * x2 - 4 * x3 >= 0)
    model.addConstr(7 * x1 + 14 * x2 <= 52)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Ringo: {x1.varValue}")
        print(f"Hours worked by Hank: {x2.varValue}")
        print(f"Hours worked by Laura: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```