## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bill', 'hours worked by Ringo', 'hours worked by Dale', and 'hours worked by George'. 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 $6.8x_1 + 2.31x_2 + 1.02x_3 + 1.49x_4$.

## Step 3: List the constraints in symbolic notation
1. $16x_1$ is not a constraint but a given value, similarly for $x_2, x_3, x_4$ which are $6, 14, 16$ respectively.
2. $6x_2 + 16x_4 \geq 20$
3. $14x_3 + 16x_4 \geq 39$
4. $16x_1 + 6x_2 \geq 30$
5. $6x_2 + 14x_3 + 16x_4 \geq 29$
6. $16x_1 + 6x_2 + 14x_3 + 16x_4 \geq 29$
7. $5x_2 - 4x_4 \geq 0$
8. $16x_1 + 6x_2 + 16x_4 \leq 128$
9. $16x_1 + 14x_3 + 16x_4 \leq 182$
10. $6x_2 + 14x_3 + 16x_4 \leq 73$

## 4: Define the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'hours worked by Bill'), ('x2', 'hours worked by Ringo'), ('x3', 'hours worked by Dale'), ('x4', 'hours worked by George')],
'objective_function': '6.8x1 + 2.31x2 + 1.02x3 + 1.49x4',
'constraints': [
'6x2 + 16x4 >= 20',
'14x3 + 16x4 >= 39',
'16x1 + 6x2 >= 30',
'6x2 + 14x3 + 16x4 >= 29',
'16x1 + 6x2 + 14x3 + 16x4 >= 29',
'5x2 - 4x4 >= 0',
'16x1 + 6x2 + 16x4 <= 128',
'16x1 + 14x3 + 16x4 <= 182',
'6x2 + 14x3 + 16x4 <= 73'
]
}
```

## 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='hours_worked_by_Bill', lb=0)
    x2 = model.addVar(name='hours_worked_by_Ringo', lb=0)
    x3 = model.addVar(name='hours_worked_by_Dale', lb=0)
    x4 = model.addVar(name='hours_worked_by_George', lb=0)

    # Define the objective function
    model.setObjective(6.8 * x1 + 2.31 * x2 + 1.02 * x3 + 1.49 * x4, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(6 * x2 + 16 * x4 >= 20)
    model.addConstr(14 * x3 + 16 * x4 >= 39)
    model.addConstr(16 * x1 + 6 * x2 >= 30)
    model.addConstr(6 * x2 + 14 * x3 + 16 * x4 >= 29)
    model.addConstr(16 * x1 + 6 * x2 + 14 * x3 + 16 * x4 >= 29)
    model.addConstr(5 * x2 - 4 * x4 >= 0)
    model.addConstr(16 * x1 + 6 * x2 + 16 * x4 <= 128)
    model.addConstr(16 * x1 + 14 * x3 + 16 * x4 <= 182)
    model.addConstr(6 * x2 + 14 * x3 + 16 * x4 <= 73)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Hours worked by Bill: ', x1.varValue)
        print('Hours worked by Ringo: ', x2.varValue)
        print('Hours worked by Dale: ', x3.varValue)
        print('Hours worked by George: ', x4.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```