## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Mary', 'hours worked by Laura', 'hours worked by Peggy', 'hours worked by John'] which can be represented symbolically as ['x0', 'x1', 'x2', 'x3'].

## Step 2: Map the variables to their natural language descriptions
The symbolic representation of the variables and their corresponding natural language descriptions are:
- x0: hours worked by Mary
- x1: hours worked by Laura
- x2: hours worked by Peggy
- x3: hours worked by John

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is: $6.59x0 + 2.27x1 + 9.41x2 + 8.96x3$.

## 4: List the constraints in symbolic notation
The constraints are:
- $1x0 \geq 0$ and $1x0 \leq 248$ (Implicit in x0's definition, but noted for clarity)
- $5x1 \geq 0$ and $5x1 \leq 248$ (Implicit in x1's definition, but noted for clarity)
- $14x2 \geq 0$ and $14x2 \leq 248$ (Implicit in x2's definition, but noted for clarity)
- $1x3 \geq 0$ and $1x3 \leq 248$ (Implicit in x3's definition, but noted for clarity)
- $1x0 + 5x1 \geq 21$
- $1x0 + 14x2 \geq 39$
- $5x1 + 14x2 + 1x3 \geq 45$
- $1x0 + 5x1 + 14x2 + 1x3 \geq 45$
- $6x1 + 4x3 \geq 13$
- $6x2 + 4x3 \geq 25$
- $6x1 + 6x2 \geq 11$
- $15x0 + 6x1 + 6x2 + 4x3 \geq 11$
- $9x2 - 4x3 \geq 0$
- $1x0 + 5x1 + 1x3 \leq 216$
- $5x1 + 14x2 + 1x3 \leq 225$
- $1x0 + 5x1 + 14x2 \leq 134$
- $15x0 + 6x1 + 6x2 \leq 84$
- $6x1 + 6x2 + 4x3 \leq 112$
- $x0 \in \mathbb{Z}$
- $x1 \in \mathbb{Z}$
- $x2 \in \mathbb{R}$
- $x3 \in \mathbb{Z}$

## 5: Create the symbolic representation dictionary
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Mary'), 
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Peggy'), 
        ('x3', 'hours worked by John')
    ], 
    'objective_function': '6.59x0 + 2.27x1 + 9.41x2 + 8.96x3', 
    'constraints': [
        '1x0 + 5x1 >= 21',
        '1x0 + 14x2 >= 39',
        '5x1 + 14x2 + 1x3 >= 45',
        '1x0 + 5x1 + 14x2 + 1x3 >= 45',
        '6x1 + 4x3 >= 13',
        '6x2 + 4x3 >= 25',
        '6x1 + 6x2 >= 11',
        '15x0 + 6x1 + 6x2 + 4x3 >= 11',
        '9x2 - 4x3 >= 0',
        '1x0 + 5x1 + 1x3 <= 216',
        '5x1 + 14x2 + 1x3 <= 225',
        '1x0 + 5x1 + 14x2 <= 134',
        '15x0 + 6x1 + 6x2 <= 84',
        '6x1 + 6x2 + 4x3 <= 112'
    ]
}
```

## 6: Write the Gurobi code
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # hours worked by Mary
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # hours worked by Laura
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.CONTINUOUS)  # hours worked by Peggy
    x3 = model.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # hours worked by John

    # Objective function
    model.setObjective(6.59 * x0 + 2.27 * x1 + 9.41 * x2 + 8.96 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x0 + 5 * x1 >= 21)
    model.addConstr(x0 + 14 * x2 >= 39)
    model.addConstr(5 * x1 + 14 * x2 + x3 >= 45)
    model.addConstr(x0 + 5 * x1 + 14 * x2 + x3 >= 45)
    model.addConstr(6 * x1 + 4 * x3 >= 13)
    model.addConstr(6 * x2 + 4 * x3 >= 25)
    model.addConstr(6 * x1 + 6 * x2 >= 11)
    model.addConstr(15 * x0 + 6 * x1 + 6 * x2 + 4 * x3 >= 11)
    model.addConstr(9 * x2 - 4 * x3 >= 0)
    model.addConstr(x0 + 5 * x1 + x3 <= 216)
    model.addConstr(5 * x1 + 14 * x2 + x3 <= 225)
    model.addConstr(x0 + 5 * x1 + 14 * x2 <= 134)
    model.addConstr(15 * x0 + 6 * x1 + 6 * x2 <= 84)
    model.addConstr(6 * x1 + 6 * x2 + 4 * x3 <= 112)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Mary: {x0.varValue}")
        print(f"Hours worked by Laura: {x1.varValue}")
        print(f"Hours worked by Peggy: {x2.varValue}")
        print(f"Hours worked by John: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```