## Step 1: Define the symbolic representation of the problem
Let's denote the number of bagels as $x_1$ and the number of burgers as $x_2$. The objective is to minimize the total cost, which is $4.5x_1 + 12x_2$. The constraints are:
- $250x_1 + 800x_2 \geq 2500$ (minimum calories per day)
- $15x_1 + 23.5x_2 \geq 500$ (minimum grams of fat per day)
- $x_1 \geq 0$ and $x_2 \geq 0$ (non-negativity constraints)

## Step 2: Express the problem in the required symbolic format
The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'bagels'), ('x2', 'burgers')],
    'objective_function': '4.5*x1 + 12*x2',
    'constraints': [
        '250*x1 + 800*x2 >= 2500',
        '15*x1 + 23.5*x2 >= 500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 3: Convert the symbolic representation into Gurobi code
Now, let's implement this problem using Gurobi in Python:

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="bagels", lb=0)  # Number of bagels
    x2 = model.addVar(name="burgers", lb=0)  # Number of burgers

    # Define the objective function
    model.setObjective(4.5 * x1 + 12 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(250 * x1 + 800 * x2 >= 2500, name="calories_constraint")
    model.addConstr(15 * x1 + 23.5 * x2 >= 500, name="fat_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal number of bagels: {x1.varValue}")
        print(f"Optimal number of burgers: {x2.varValue}")
        print(f"Optimal cost: {model.objVal}")
    else:
        print("The model is infeasible")

solve_optimization_problem()
```