To solve the peanut farmer's problem, we need to formulate a linear programming (LP) model that maximizes the number of peanut packages transported under the given constraints. Let's define the decision variables and the objective function.

- Decision Variables:
  - \(x_t\): Number of trips by train.
  - \(x_{tr}\): Number of trips by truck.
  
- Objective Function: Maximize the total number of packages transported, which can be represented as \(80x_t + 50x_{tr}\).

- Constraints:
  1. The total cost constraint: \(50x_t + 40x_{tr} \leq 3000\).
  2. The train trips vs. truck trips constraint: \(x_t \leq x_{tr}\).
  3. Non-negativity constraints: \(x_t \geq 0, x_{tr} \geq 0\).

Since the problem involves maximizing the number of packages and all coefficients are positive, we don't need to explicitly consider lower bounds for \(x_t\) and \(x_{tr}\) other than them being non-negative.

Now, let's translate this LP formulation into Gurobi code in Python:

```python
from gurobipy import *

# Create a model
m = Model("Peanut_Transportation")

# Define the decision variables
x_train = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Train_Trips")
x_truck = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Truck_Trips")

# Set the objective function: Maximize the total number of packages transported
m.setObjective(80*x_train + 50*x_truck, GRB.MAXIMIZE)

# Add constraints
m.addConstr(50*x_train + 40*x_truck <= 3000, "Total_Cost_Constraint")
m.addConstr(x_train <= x_truck, "Train_vs_Truck_Trips")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Maximum number of packages that can be transported: {m.objVal}")
    print(f"Number of train trips: {x_train.x}")
    print(f"Number of truck trips: {x_truck.x}")
else:
    print("Model is infeasible or unbounded.")
```