## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Ringo', 'hours worked by George', 'hours worked by Laura', 'hours worked by Dale']. Let's denote them as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $8x_1 + 4x_2 + 6x_3 + 9x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $0.08x_1 \leq 548$
- $2.32x_2 \leq 548$
- $2.81x_3 \leq 548$
- $2.59x_4 \leq 548$
- $0.08x_1 + 2.81x_3 \geq 131$
- $2.32x_2 + 2.81x_3 + 2.59x_4 \geq 111$
- $0.08x_1 + 2.32x_2 + 2.81x_3 \geq 111$
- $2.32x_2 + 2.81x_3 + 2.59x_4 \geq 127$
- $0.08x_1 + 2.32x_2 + 2.81x_3 \geq 127$
- $0.08x_1 + 2.32x_2 + 2.81x_3 + 2.59x_4 \geq 127$
- $-5x_3 + 9x_4 \geq 0$
- $8x_1 - 5x_3 \geq 0$
- $0.08x_1 + 2.59x_4 \leq 262$
- $2.81x_3 + 2.59x_4 \leq 431$
- $0.08x_1 + 2.32x_2 + 2.59x_4 \leq 245$
- $x_1$ is an integer
- $x_2$ is an integer
- $x_3$ is an integer
- $x_4$ is a real number

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Ringo'), 
        ('x2', 'hours worked by George'), 
        ('x3', 'hours worked by Laura'), 
        ('x4', 'hours worked by Dale')
    ], 
    'objective_function': '8*x1 + 4*x2 + 6*x3 + 9*x4', 
    'constraints': [
        '0.08*x1 <= 548',
        '2.32*x2 <= 548',
        '2.81*x3 <= 548',
        '2.59*x4 <= 548',
        '0.08*x1 + 2.81*x3 >= 131',
        '2.32*x2 + 2.81*x3 + 2.59*x4 >= 111',
        '0.08*x1 + 2.32*x2 + 2.81*x3 >= 111',
        '2.32*x2 + 2.81*x3 + 2.59*x4 >= 127',
        '0.08*x1 + 2.32*x2 + 2.81*x3 >= 127',
        '0.08*x1 + 2.32*x2 + 2.81*x3 + 2.59*x4 >= 127',
        '-5*x3 + 9*x4 >= 0',
        '8*x1 - 5*x3 >= 0',
        '0.08*x1 + 2.59*x4 <= 262',
        '2.81*x3 + 2.59*x4 <= 431',
        '0.08*x1 + 2.32*x2 + 2.59*x4 <= 245'
    ],
    'integrality_constraints': [
        'x1', 'x2', 'x3'
    ]
}
```

## 5: 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='x1', vtype=gurobi.GRB.INTEGER)  # hours worked by Ringo
    x2 = model.addVar(name='x2', vtype=gurobi.GRB.INTEGER)  # hours worked by George
    x3 = model.addVar(name='x3', vtype=gurobi.GRB.INTEGER)  # hours worked by Laura
    x4 = model.addVar(name='x4')  # hours worked by Dale

    # Define the objective function
    model.setObjective(8 * x1 + 4 * x2 + 6 * x3 + 9 * x4, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(0.08 * x1 <= 548)
    model.addConstr(2.32 * x2 <= 548)
    model.addConstr(2.81 * x3 <= 548)
    model.addConstr(2.59 * x4 <= 548)
    model.addConstr(0.08 * x1 + 2.81 * x3 >= 131)
    model.addConstr(2.32 * x2 + 2.81 * x3 + 2.59 * x4 >= 111)
    model.addConstr(0.08 * x1 + 2.32 * x2 + 2.81 * x3 >= 111)
    model.addConstr(2.32 * x2 + 2.81 * x3 + 2.59 * x4 >= 127)
    model.addConstr(0.08 * x1 + 2.32 * x2 + 2.81 * x3 >= 127)
    model.addConstr(0.08 * x1 + 2.32 * x2 + 2.81 * x3 + 2.59 * x4 >= 127)
    model.addConstr(-5 * x3 + 9 * x4 >= 0)
    model.addConstr(8 * x1 - 5 * x3 >= 0)
    model.addConstr(0.08 * x1 + 2.59 * x4 <= 262)
    model.addConstr(2.81 * x3 + 2.59 * x4 <= 431)
    model.addConstr(0.08 * x1 + 2.32 * x2 + 2.59 * x4 <= 245)

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('x1: ', x1.varValue)
        print('x2: ', x2.varValue)
        print('x3: ', x3.varValue)
        print('x4: ', x4.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```