## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George', 'hours worked by Bill', 'hours worked by Peggy', 'hours worked by Ringo', which can be represented symbolically as $x_0$, $x_1$, $x_2$, $x_3$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $1.9x_0 + 2.09x_1 + 5.6x_2 + 2.2x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $4x_1 + 2x_3 \geq 13$
- $4x_1 + 11x_2 + 2x_3 \geq 15$
- $7x_0 + 11x_2 + 2x_3 \geq 15$
- $7x_0 + 4x_1 + 11x_2 \geq 15$
- $4x_1 + 11x_2 + 2x_3 \geq 21$
- $7x_0 + 11x_2 + 2x_3 \geq 21$
- $7x_0 + 4x_1 + 11x_2 \geq 21$
- $4x_1 + 11x_2 + 2x_3 \geq 17$
- $7x_0 + 11x_2 + 2x_3 \geq 17$
- $7x_0 + 4x_1 + 11x_2 \geq 17$
- $3x_1 + 6x_2 + 8x_3 \geq 19$
- $4x_1 + 11x_2 \leq 92$
- $7x_0 + 11x_2 \leq 58$
- $11x_2 + 2x_3 \leq 84$
- $7x_0 + 4x_1 + 11x_2 \leq 54$
- $7x_0 + 4x_1 + 11x_2 + 2x_3 \leq 54$
- $3x_1 + 6x_2 \leq 27$
- $3x_1 + 8x_3 \leq 73$
- $8x_0 + 8x_3 \leq 37$
- $6x_2 + 8x_3 \leq 73$
- $8x_0 + 3x_1 + 6x_2 + 8x_3 \leq 73$

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by George'), 
        ('x1', 'hours worked by Bill'), 
        ('x2', 'hours worked by Peggy'), 
        ('x3', 'hours worked by Ringo')
    ], 
    'objective_function': '1.9*x0 + 2.09*x1 + 5.6*x2 + 2.2*x3', 
    'constraints': [
        '4*x1 + 2*x3 >= 13',
        '4*x1 + 11*x2 + 2*x3 >= 15',
        '7*x0 + 11*x2 + 2*x3 >= 15',
        '7*x0 + 4*x1 + 11*x2 >= 15',
        '4*x1 + 11*x2 + 2*x3 >= 21',
        '7*x0 + 11*x2 + 2*x3 >= 21',
        '7*x0 + 4*x1 + 11*x2 >= 21',
        '4*x1 + 11*x2 + 2*x3 >= 17',
        '7*x0 + 11*x2 + 2*x3 >= 17',
        '7*x0 + 4*x1 + 11*x2 >= 17',
        '3*x1 + 6*x2 + 8*x3 >= 19',
        '4*x1 + 11*x2 <= 92',
        '7*x0 + 11*x2 <= 58',
        '11*x2 + 2*x3 <= 84',
        '7*x0 + 4*x1 + 11*x2 <= 54',
        '7*x0 + 4*x1 + 11*x2 + 2*x3 <= 54',
        '3*x1 + 6*x2 <= 27',
        '3*x1 + 8*x3 <= 73',
        '8*x0 + 8*x3 <= 37',
        '6*x2 + 8*x3 <= 73',
        '8*x0 + 3*x1 + 6*x2 + 8*x3 <= 73'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by George
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Bill
    x2 = model.addVar(name="x2", lb=0)  # hours worked by Peggy
    x3 = model.addVar(name="x3", lb=0)  # hours worked by Ringo

    # Define the objective function
    model.setObjective(1.9*x0 + 2.09*x1 + 5.6*x2 + 2.2*x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4*x1 + 2*x3 >= 13)
    model.addConstr(4*x1 + 11*x2 + 2*x3 >= 15)
    model.addConstr(7*x0 + 11*x2 + 2*x3 >= 15)
    model.addConstr(7*x0 + 4*x1 + 11*x2 >= 15)
    model.addConstr(4*x1 + 11*x2 + 2*x3 >= 21)
    model.addConstr(7*x0 + 11*x2 + 2*x3 >= 21)
    model.addConstr(7*x0 + 4*x1 + 11*x2 >= 21)
    model.addConstr(4*x1 + 11*x2 + 2*x3 >= 17)
    model.addConstr(7*x0 + 11*x2 + 2*x3 >= 17)
    model.addConstr(7*x0 + 4*x1 + 11*x2 >= 17)
    model.addConstr(3*x1 + 6*x2 + 8*x3 >= 19)
    model.addConstr(4*x1 + 11*x2 <= 92)
    model.addConstr(7*x0 + 11*x2 <= 58)
    model.addConstr(11*x2 + 2*x3 <= 84)
    model.addConstr(7*x0 + 4*x1 + 11*x2 <= 54)
    model.addConstr(7*x0 + 4*x1 + 11*x2 + 2*x3 <= 54)
    model.addConstr(3*x1 + 6*x2 <= 27)
    model.addConstr(3*x1 + 8*x3 <= 73)
    model.addConstr(8*x0 + 8*x3 <= 37)
    model.addConstr(6*x2 + 8*x3 <= 73)
    model.addConstr(8*x0 + 3*x1 + 6*x2 + 8*x3 <= 73)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by George: ", x0.varValue)
        print("Hours worked by Bill: ", x1.varValue)
        print("Hours worked by Peggy: ", x2.varValue)
        print("Hours worked by Ringo: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```