## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

- Let \(x_1\) be the number of almond tins.
- Let \(x_2\) be the number of cashew tins.

The objective is to maximize profit. Given that the profit per almond tin is $10 and per cashew tin is $15, the objective function can be represented as:

\[ \text{Maximize:} \quad 10x_1 + 15x_2 \]

The constraints are based on the time available for filling and labeling:

- Each almond tin takes 5 minutes to fill and each cashew tin takes 4 minutes to fill. With 400 minutes available for filling:
\[ 5x_1 + 4x_2 \leq 400 \]

- Each almond tin takes 3 minutes to label and each cashew tin takes 5 minutes to label. With 500 minutes available for labeling:
\[ 3x_1 + 5x_2 \leq 500 \]

Also, \(x_1 \geq 0\) and \(x_2 \geq 0\) because the number of tins cannot be negative.

## Symbolic Representation in JSON Format

```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'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Almond_Cashew_Optimization")

# Define the variables
x1 = model.addVar(name="almond_tins", lb=0, vtype=gp.GRB.INTEGER)
x2 = model.addVar(name="cashew_tins", lb=0, vtype=gp.GRB.INTEGER)

# Define the objective function
model.setObjective(10*x1 + 15*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(5*x1 + 4*x2 <= 400, name="filling_time_constraint")
model.addConstr(3*x1 + 5*x2 <= 500, name="labeling_time_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: Almond tins = {x1.varValue}, Cashew tins = {x2.varValue}")
    print(f"Maximum profit: ${10*x1.varValue + 15*x2.varValue}")
else:
    print("The model is infeasible.")
```