## Problem Description and Formulation

The farm needs to transport chickens using trains and trucks. The goal is to maximize the number of chickens transported given certain constraints.

- Each train trip can take 500 chickens and costs $100.
- Each truck trip can take 300 chickens and costs $80.
- The farm has a budget of $2000.
- The number of train trips cannot exceed the number of truck trips.

## Symbolic Representation

Let's denote:
- \(T\) as the number of train trips.
- \(K\) as the number of truck trips.

The objective is to maximize the total number of chickens transported:
\[ \text{Maximize:} \quad 500T + 300K \]

Subject to:
1. Budget constraint: \( 100T + 80K \leq 2000 \)
2. Train trips constraint: \( T \leq K \)
3. Non-negativity constraint: \( T \geq 0, K \geq 0 \) and \( T, K \) are integers.

## Gurobi Code

Since the problem involves integer solutions, it's an Integer Linear Programming (ILP) problem. Here's how to formulate and solve it using Gurobi in Python:

```python
import gurobi

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

    # Define variables: T (train trips) and K (truck trips)
    T = model.addVar(name="T", vtype=gurobi.GRB.INTEGER, lb=0)
    K = model.addVar(name="K", vtype=gurobi.GRB.INTEGER, lb=0)

    # Objective: Maximize 500T + 300K
    model.setObjective(500*T + 300*K, gurobi.GRB.MAXIMIZE)

    # Budget constraint: 100T + 80K <= 2000
    model.addConstr(100*T + 80*K <= 2000, name="budget_constraint")

    # Train trips cannot exceed truck trips: T <= K
    model.addConstr(T <= K, name="train_truck_constraint")

    # Solve the model
    model.optimize()

    # Print the status
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print(f"Optimal solution: Train trips = {T.varValue}, Truck trips = {K.varValue}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("The problem is infeasible.")
    else:
        print("The model status is not optimal or infeasible.")

solve_transportation_problem()
```

This code sets up the optimization problem as described, solves it using Gurobi, and prints out the optimal solution or indicates if the problem is infeasible.