To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of almond tins sold,
- $x_2$ as the number of cashew tins sold.

The objective is to maximize profit. Given that each almond tin yields a profit of $10 and each cashew tin yields a profit of $15, the objective function can be written as:
\[ \text{Maximize:} \quad 10x_1 + 15x_2 \]

Now, let's consider the constraints:
1. Time constraint for filling tins: Each almond tin takes 5 minutes to fill, and each cashew tin takes 4 minutes to fill. The company has available 400 minutes for filling.
\[ 5x_1 + 4x_2 \leq 400 \]
2. Time constraint for labeling tins: Each almond tin takes 3 minutes to label, and each cashew tin takes 5 minutes to label. The company has available 500 minutes for labeling.
\[ 3x_1 + 5x_2 \leq 500 \]
3. Non-negativity constraints: Since the number of tins cannot be negative,
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

In symbolic notation, our problem can be represented as:
```json
{
  'sym_variables': [('x1', 'almond tins'), ('x2', 'cashew tins')],
  'objective_function': '10*x1 + 15*x2',
  'constraints': ['5*x1 + 4*x2 <= 400', '3*x1 + 5*x2 <= 500', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we can write the following code:
```python
from gurobipy import *

# Create a new model
m = Model("Almond_Cashew_Optimization")

# Define variables
x1 = m.addVar(name="almond_tins", vtype=GRB.CONTINUOUS, lb=0)
x2 = m.addVar(name="cashew_tins", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
m.setObjective(10*x1 + 15*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 4*x2 <= 400, name="filling_time")
m.addConstr(3*x1 + 5*x2 <= 500, name="labeling_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Almond tins: {x1.x}")
    print(f"Cashew tins: {x2.x}")
    print(f"Maximum profit: ${10*x1.x + 15*x2.x:.2f}")
else:
    print("No optimal solution found")
```