## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Peggy' and 'hours worked by Bill', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $3.66x_1 + 2.91x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $0.81x_1 + 21.75x_2 \geq 69$
2. $2x_1 - 3x_2 \geq 0$
3. $0.81x_1 + 21.75x_2 \leq 168$
4. The variables $x_1$ and $x_2$ are not restricted to integers.

## 4: Express the problem in the required JSON format
```json
{
'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Bill')], 
'objective_function': '3.66*x1 + 2.91*x2', 
'constraints': [
    '0.81*x1 + 21.75*x2 >= 69', 
    '2*x1 - 3*x2 >= 0', 
    '0.81*x1 + 21.75*x2 <= 168'
    ]
}
```

## 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_Peggy', lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name='hours_worked_by_Bill', lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(3.66 * x1 + 2.91 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.81 * x1 + 21.75 * x2 >= 69)
    model.addConstr(2 * x1 - 3 * x2 >= 0)
    model.addConstr(0.81 * x1 + 21.75 * x2 <= 168)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```