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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $3.08x_1 + 8.47x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $12x_1 + 19x_2 \geq 11$
2. $23x_1 + 12x_2 \geq 22$
3. $-10x_1 + 6x_2 \geq 0$
4. $12x_1 + 19x_2 \leq 47$
5. $23x_1 + 12x_2 \leq 29$

## 4: Consider the bounds of the variables
The problem mentions that there are no explicit lower bounds given for $x_1$ and $x_2$, but it implies that $x_1, x_2 \geq 0$ since hours worked cannot be negative.

## 5: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by John')],
'objective_function': '3.08*x1 + 8.47*x2',
'constraints': [
'12*x1 + 19*x2 >= 11',
'23*x1 + 12*x2 >= 22',
'-10*x1 + 6*x2 >= 0',
'12*x1 + 19*x2 <= 47',
'23*x1 + 12*x2 <= 29',
'x1 >= 0',
'x2 >= 0'
]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_Ringo", lb=0)
    x2 = model.addVar(name="hours_worked_by_John", lb=0)

    # Define the objective function
    model.setObjective(3.08 * x1 + 8.47 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(12 * x1 + 19 * x2 >= 11)
    model.addConstr(23 * x1 + 12 * x2 >= 22)
    model.addConstr(-10 * x1 + 6 * x2 >= 0)
    model.addConstr(12 * x1 + 19 * x2 <= 47)
    model.addConstr(23 * x1 + 12 * x2 <= 29)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```