To solve this problem, we first need to define the decision variables and the objective function. Let's denote the number of trains as \(T\) and the number of planes as \(P\). The profit per train is $50, and the profit per plane is $60. Therefore, the total profit can be represented as \(50T + 60P\).

The constraints are:
1. Time constraint: Each train takes 30 minutes, and each plane takes 40 minutes of woodworker time. The store has 4000 minutes available. So, \(30T + 40P \leq 4000\).
2. Production ratio constraint: The store must make at least thrice the number of planes as trains. This can be represented as \(P \geq 3T\).

We also know that \(T \geq 0\) and \(P \geq 0\) because we cannot produce a negative number of items.

The objective is to maximize profit, so we want to find the values of \(T\) and \(P\) that make \(50T + 60P\) as large as possible under these constraints.

Here's how we can represent this problem in Gurobi Python code:

```python
from gurobipy import *

# Create a model
m = Model("Wooden Toys Production")

# Define the decision variables
T = m.addVar(vtype=GRB.INTEGER, name="Trains")
P = m.addVar(vtype=GRB.INTEGER, name="Planes")

# Objective function: Maximize profit
m.setObjective(50*T + 60*P, GRB.MAXIMIZE)

# Constraints
m.addConstr(30*T + 40*P <= 4000, "Time constraint")
m.addConstr(P >= 3*T, "Production ratio constraint")
m.addConstr(T >= 0, "Non-negativity of Trains")
m.addConstr(P >= 0, "Non-negativity of Planes")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Trains: {T.x}")
    print(f"Planes: {P.x}")
    print(f"Maximum profit: ${50*T.x + 60*P.x:.2f}")
else:
    print("No optimal solution found.")
```