## Step 1: Define the symbolic representation of the problem

Let's denote the number of tea tins as $x_1$ and the number of coffee tins as $x_2$. The profit per tea tin is $11, and the profit per coffee tin is $13. The time to fill a tea tin is 4 minutes, and the time to fill a coffee tin is 3 minutes, with 500 minutes available for filling. The time to label a tea tin is 1 minute, and the time to label a coffee tin is 2 minutes, with 600 minutes available for labeling.

## Step 2: Formulate the objective function

The objective is to maximize profit, which can be represented as $11x_1 + 13x_2$.

## 3: Define the constraints

The constraints based on the given resources are:
1. Filling time constraint: $4x_1 + 3x_2 \leq 500$
2. Labeling time constraint: $x_1 + 2x_2 \leq 600$
Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of tins cannot be negative.

## 4: Symbolic representation in JSON format

```json
{
    'sym_variables': [('x1', 'tea tins'), ('x2', 'coffee tins')],
    'objective_function': '11*x1 + 13*x2',
    'constraints': [
        '4*x1 + 3*x2 <= 500',
        'x1 + 2*x2 <= 600',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Convert the problem into Gurobi code

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="tea_tins")
    x2 = model.addVar(lb=0, name="coffee_tins")

    # Define the objective function
    model.setObjective(11*x1 + 13*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(4*x1 + 3*x2 <= 500, name="filling_time_constraint")
    model.addConstr(x1 + 2*x2 <= 600, name="labeling_time_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of tea tins: {x1.varValue}")
        print(f"Number of coffee tins: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```