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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $8.56x_0 + 5.65x_1 + 7.58x_2 + 7.27x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $6.26x_0 \leq 137$
- $0.76x_0 \leq 235$
- $1.6x_1 \leq 137$
- $5.92x_1 \leq 235$
- $5.57x_2 \leq 137$
- $4.04x_2 \leq 235$
- $3.99x_3 \leq 137$
- $5.11x_3 \leq 235$
- $1.6x_1 + 3.99x_3 \geq 11$
- $6.26x_0 + 1.6x_1 \geq 31$
- $1.6x_1 + 5.57x_2 \geq 26$
- $5.57x_2 + 3.99x_3 \geq 30$
- $6.26x_0 + 1.6x_1 + 5.57x_2 + 3.99x_3 \geq 30$
- $0.76x_0 + 4.04x_2 \geq 51$
- $4.04x_2 + 5.11x_3 \geq 50$
- $0.76x_0 + 5.92x_1 \geq 26$
- $5.92x_1 + 4.04x_2 \geq 36$
- $0.76x_0 + 5.92x_1 + 4.04x_2 + 5.11x_3 \geq 36$
- $-5x_0 + 5x_3 \geq 0$
- $1.6x_1 + 3.99x_3 \leq 50$
- $6.26x_0 + 5.57x_2 \leq 95$
- $1.6x_1 + 5.57x_2 \leq 79$
- $6.26x_0 + 5.57x_2 + 3.99x_3 \leq 99$
- $5.92x_1 + 4.04x_2 \leq 75$
- $5.92x_1 + 5.11x_3 \leq 174$
- $0.76x_0 + 4.04x_2 \leq 227$
- $0.76x_0 + 5.92x_1 \leq 188$
- $4.04x_2 + 5.11x_3 \leq 67$

## Step 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Mary'), 
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Ringo'), 
        ('x3', 'hours worked by John')
    ], 
    'objective_function': '8.56*x0 + 5.65*x1 + 7.58*x2 + 7.27*x3', 
    'constraints': [
        '6.26*x0 <= 137',
        '0.76*x0 <= 235',
        '1.6*x1 <= 137',
        '5.92*x1 <= 235',
        '5.57*x2 <= 137',
        '4.04*x2 <= 235',
        '3.99*x3 <= 137',
        '5.11*x3 <= 235',
        '1.6*x1 + 3.99*x3 >= 11',
        '6.26*x0 + 1.6*x1 >= 31',
        '1.6*x1 + 5.57*x2 >= 26',
        '5.57*x2 + 3.99*x3 >= 30',
        '6.26*x0 + 1.6*x1 + 5.57*x2 + 3.99*x3 >= 30',
        '0.76*x0 + 4.04*x2 >= 51',
        '4.04*x2 + 5.11*x3 >= 50',
        '0.76*x0 + 5.92*x1 >= 26',
        '5.92*x1 + 4.04*x2 >= 36',
        '0.76*x0 + 5.92*x1 + 4.04*x2 + 5.11*x3 >= 36',
        '-5*x0 + 5*x3 >= 0',
        '1.6*x1 + 3.99*x3 <= 50',
        '6.26*x0 + 5.57*x2 <= 95',
        '1.6*x1 + 5.57*x2 <= 79',
        '6.26*x0 + 5.57*x2 + 3.99*x3 <= 99',
        '5.92*x1 + 4.04*x2 <= 75',
        '5.92*x1 + 5.11*x3 <= 174',
        '0.76*x0 + 4.04*x2 <= 227',
        '0.76*x0 + 5.92*x1 <= 188',
        '4.04*x2 + 5.11*x3 <= 67'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name='x0', lb=0)  # hours worked by Mary
    x1 = model.addVar(name='x1', lb=0)  # hours worked by Laura
    x2 = model.addVar(name='x2', lb=0)  # hours worked by Ringo
    x3 = model.addVar(name='x3', lb=0, integrality=0)  # hours worked by John

    # Define the objective function
    model.setObjective(8.56 * x0 + 5.65 * x1 + 7.58 * x2 + 7.27 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(6.26 * x0 <= 137)
    model.addConstr(0.76 * x0 <= 235)
    model.addConstr(1.6 * x1 <= 137)
    model.addConstr(5.92 * x1 <= 235)
    model.addConstr(5.57 * x2 <= 137)
    model.addConstr(4.04 * x2 <= 235)
    model.addConstr(3.99 * x3 <= 137)
    model.addConstr(5.11 * x3 <= 235)
    model.addConstr(1.6 * x1 + 3.99 * x3 >= 11)
    model.addConstr(6.26 * x0 + 1.6 * x1 >= 31)
    model.addConstr(1.6 * x1 + 5.57 * x2 >= 26)
    model.addConstr(5.57 * x2 + 3.99 * x3 >= 30)
    model.addConstr(6.26 * x0 + 1.6 * x1 + 5.57 * x2 + 3.99 * x3 >= 30)
    model.addConstr(0.76 * x0 + 4.04 * x2 >= 51)
    model.addConstr(4.04 * x2 + 5.11 * x3 >= 50)
    model.addConstr(0.76 * x0 + 5.92 * x1 >= 26)
    model.addConstr(5.92 * x1 + 4.04 * x2 >= 36)
    model.addConstr(0.76 * x0 + 5.92 * x1 + 4.04 * x2 + 5.11 * x3 >= 36)
    model.addConstr(-5 * x0 + 5 * x3 >= 0)
    model.addConstr(1.6 * x1 + 3.99 * x3 <= 50)
    model.addConstr(6.26 * x0 + 5.57 * x2 <= 95)
    model.addConstr(1.6 * x1 + 5.57 * x2 <= 79)
    model.addConstr(6.26 * x0 + 5.57 * x2 + 3.99 * x3 <= 99)
    model.addConstr(5.92 * x1 + 4.04 * x2 <= 75)
    model.addConstr(5.92 * x1 + 5.11 * x3 <= 174)
    model.addConstr(0.76 * x0 + 4.04 * x2 <= 227)
    model.addConstr(0.76 * x0 + 5.92 * x1 <= 188)
    model.addConstr(4.04 * x2 + 5.11 * x3 <= 67)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Hours worked by Mary: ', x0.varValue)
        print('Hours worked by Laura: ', x1.varValue)
        print('Hours worked by Ringo: ', x2.varValue)
        print('Hours worked by John: ', x3.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```