## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. Let's define the symbolic variables:
- $x_0$ represents 'hours worked by Laura'
- $x_1$ represents 'hours worked by Mary'
- $x_2$ represents 'hours worked by Ringo'

The objective function to maximize is $8x_0 + 6x_1 + 5x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $4x_0 \geq 4$ (Laura's likelihood to quit index is 4, but this seems to be a given condition rather than a constraint on $x_0$)
- $3x_0$ (Laura's dollar cost per hour is 3, again a given condition)
- $11x_1$ (Mary's likelihood to quit index is 11, a given condition)
- $6x_1$ (Mary's dollar cost per hour is 6, a given condition)
- $3x_2$ (Ringo's likelihood to quit index is 3, a given condition)
- $8x_2$ (Ringo's dollar cost per hour is 8, a given condition)
- $4x_0 + 3x_2 \geq 12$ (total combined likelihood to quit index from hours worked by Laura and Ringo)
- $4x_0 + 11x_1 \leq 36$ (total combined likelihood to quit index from hours worked by Laura and Mary)
- $11x_1 + 3x_2 \leq 47$ (total combined likelihood to quit index from hours worked by Mary and Ringo)
- $4x_0 + 11x_1 + 3x_2 \leq 47$ (total combined likelihood to quit index from all)
- $6x_1 + 8x_2 \leq 48$ (total combined dollar cost per hour from hours worked by Mary and Ringo)
- $3x_0 + 8x_2 \leq 60$ (total combined dollar cost per hour from hours worked by Laura and Ringo)
- $3x_0 + 6x_1 + 8x_2 \leq 25$ (total combined dollar cost per hour from all)
- $x_0$ is an integer (hours worked by Laura must be a whole number)
- $x_1$ and $x_2$ can be non-integers

## 3: Correct and refine the constraints based on the problem statement
Given conditions should not be directly included as constraints but rather as part of the problem definition. The actual constraints to consider are:
- $4x_0 + 3x_2 \geq 12$
- $4x_0 + 11x_1 \leq 36$
- $11x_1 + 3x_2 \leq 47$
- $4x_0 + 11x_1 + 3x_2 \leq 47$
- $6x_1 + 8x_2 \leq 48$
- $3x_0 + 8x_2 \leq 60$
- $3x_0 + 6x_1 + 8x_2 \leq 25$

## 4: Define the symbolic representation
```json
{
    'sym_variables': [('x0', 'hours worked by Laura'), ('x1', 'hours worked by Mary'), ('x2', 'hours worked by Ringo')],
    'objective_function': '8*x0 + 6*x1 + 5*x2',
    'constraints': [
        '4*x0 + 3*x2 >= 12',
        '4*x0 + 11*x1 <= 36',
        '11*x1 + 3*x2 <= 47',
        '4*x0 + 11*x1 + 3*x2 <= 47',
        '6*x1 + 8*x2 <= 48',
        '3*x0 + 8*x2 <= 60',
        '3*x0 + 6*x1 + 8*x2 <= 25',
        'x0 >= 0', 'x1 >= 0', 'x2 >= 0'
    ]
}
```

## 5: Implement the problem in Gurobi
```python
import gurobi

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

    # Define 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

    # Objective function
    model.setObjective(8*x0 + 6*x1 + 5*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(4*x0 + 3*x2 >= 12)
    model.addConstr(4*x0 + 11*x1 <= 36)
    model.addConstr(11*x1 + 3*x2 <= 47)
    model.addConstr(4*x0 + 11*x1 + 3*x2 <= 47)
    model.addConstr(6*x1 + 8*x2 <= 48)
    model.addConstr(3*x0 + 8*x2 <= 60)
    model.addConstr(3*x0 + 6*x1 + 8*x2 <= 25)
    model.addConstr(x0 >= 0)
    model.addConstr(x1 >= 0)
    model.addConstr(x2 >= 0)

    # Optimize
    model.optimize()

    # Print 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 problem is infeasible")

solve_optimization_problem()
```