## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of trains.
- $x_2$ represents the number of planes.

## Step 2: Translate the objective function into symbolic notation
The profit per train is $50, and the profit per plane is $60. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 50x_1 + 60x_2 \]

## 3: Translate the constraints into symbolic notation
1. Each train takes 30 minutes of woodworker time, and each plane takes 40 minutes. The store has 4000 minutes available:
\[ 30x_1 + 40x_2 \leq 4000 \]
2. The store must make at least thrice the number of planes as trains:
\[ x_2 \geq 3x_1 \]
3. Non-negativity constraints (number of trains and planes cannot be negative):
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'trains'), ('x2', 'planes')],
'objective_function': '50*x1 + 60*x2',
'constraints': [
    '30*x1 + 40*x2 <= 4000',
    'x2 >= 3*x1',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Write the Gurobi code to solve the problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="trains", lb=0, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="planes", lb=0, vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(50 * x1 + 60 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(30 * x1 + 40 * x2 <= 4000, name="woodworker_time")
    model.addConstr(x2 >= 3 * x1, name="plane_train_ratio")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```