## Step 1: Define the symbolic representation of the variables
The variables are 'slices of pizza' and 'chicken breasts', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $4.05x_1 + 6.13x_2$.

## Step 3: Convert the constraints into a symbolic representation
The constraints are:
1. $18x_1 + 15x_2 \geq 101$
2. $8x_1 - 4x_2 \geq 0$
3. $18x_1 + 15x_2 \leq 177$
4. $x_1, x_2 \geq 0$ (Implicit, as quantities cannot be negative)

## 4: Define the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'slices of pizza'), ('x2', 'chicken breasts')],
'objective_function': '4.05*x1 + 6.13*x2',
'constraints': [
    '18*x1 + 15*x2 >= 101',
    '8*x1 - 4*x2 >= 0',
    '18*x1 + 15*x2 <= 177'
]
}
```

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

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

    # Define the variables
    x1 = model.addVar(name="slices_of_pizza", lb=0)  # slices of pizza
    x2 = model.addVar(name="chicken_breasts", lb=0)  # chicken breasts

    # Define the objective function
    model.setObjective(4.05 * x1 + 6.13 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(18 * x1 + 15 * x2 >= 101)
    model.addConstr(8 * x1 - 4 * x2 >= 0)
    model.addConstr(18 * x1 + 15 * x2 <= 177)

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Slices of pizza: {x1.x}")
        print(f"Chicken breasts: {x2.x}")
        print(f"Objective function value: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

optimize_problem()
```