To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function along with the constraints.

### Symbolic Representation:

Let:
- $x_1$ be the number of train trips.
- $x_2$ be the number of truck trips.

The objective is to maximize the total number of peanut packages transported, which can be represented as $80x_1 + 50x_2$ since each train trip can take 80 packages and each truck trip can take 50 packages.

The constraints are:
1. The cost constraint: $50x_1 + 40x_2 \leq 3000$, because the farmer wants to spend at most $3000.
2. The trip constraint: $x_1 \leq x_2$, because the number of train trips must not exceed the number of truck trips.
3. Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$, since the number of trips cannot be negative.

### Symbolic Representation in JSON Format:
```json
{
    'sym_variables': [('x1', 'number of train trips'), ('x2', 'number of truck trips')],
    'objective_function': '80*x1 + 50*x2',
    'constraints': ['50*x1 + 40*x2 <= 3000', 'x1 <= x2', 'x1 >= 0', 'x2 >= 0']
}
```

### Gurobi Code in Python:
To solve this linear programming problem using Gurobi, we can use the following Python code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="train_trips")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="truck_trips")

# Set the objective function
m.setObjective(80*x1 + 50*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(50*x1 + 40*x2 <= 3000, "cost_constraint")
m.addConstr(x1 <= x2, "trip_constraint")
m.addConstr(x1 >= 0, "non_neg_train_trips")
m.addConstr(x2 >= 0, "non_neg_truck_trips")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of train trips: {x1.x}")
    print(f"Number of truck trips: {x2.x}")
    print(f"Total packages transported: {80*x1.x + 50*x2.x}")
else:
    print("No optimal solution found")
```