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

Let's define the symbolic variables:
- $x_1$ represents the number of train trips
- $x_2$ represents the number of truck trips

The objective is to maximize the total number of chickens transported. Each train trip can take 500 chickens, and each truck trip can take 300 chickens. Therefore, the objective function is $500x_1 + 300x_2$.

## Step 2: Define the constraints

The farm has a budget of $2000. The cost per train trip is $100, and the cost per truck trip is $80. This gives us the budget constraint: $100x_1 + 80x_2 \leq 2000$.

The number of train trips cannot exceed the number of truck trips: $x_1 \leq x_2$.

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of trips cannot be negative.

## 3: Convert the problem into a symbolic representation

```json
{
    'sym_variables': [('x1', 'train trips'), ('x2', 'truck trips')],
    'objective_function': '500*x1 + 300*x2',
    'constraints': [
        '100*x1 + 80*x2 <= 2000',
        'x1 <= x2',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 4: Implement the problem in Gurobi code

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(vtype=gurobi.GRB.INTEGER, name="train_trips")
    x2 = model.addVar(vtype=gurobi.GRB.INTEGER, name="truck_trips")

    # Objective function: maximize 500*x1 + 300*x2
    model.setObjective(500*x1 + 300*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(100*x1 + 80*x2 <= 2000, name="budget_constraint")
    model.addConstr(x1 <= x2, name="train_truck_constraint")
    model.addConstr(x1 >= 0, name="non_negativity_train")
    model.addConstr(x2 >= 0, name="non_negativity_truck")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of train trips: {x1.varValue}")
        print(f"Number of truck trips: {x2.varValue}")
        print(f"Total chickens transported: {500*x1.varValue + 300*x2.varValue}")
    else:
        print("No optimal solution found.")

solve_transportation_problem()
```