## Problem Description and Symbolic Representation

The problem involves a peanut farmer who needs to transport peanut packages to the city using trains and trucks. The goal is to maximize the number of packages transported under certain constraints.

### Symbolic Variables:
- $x_1$ = number of train trips
- $x_2$ = number of truck trips

### Objective Function:
Maximize the total number of peanut packages transported: $80x_1 + 50x_2$

### Constraints:
1. Cost constraint: $50x_1 + 40x_2 \leq 3000$
2. Trip constraint: $x_1 \leq x_2$
3. Non-negativity constraint: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'train trips'), ('x2', 'truck trips')],
    'objective_function': '80*x1 + 50*x2',
    'constraints': [
        '50*x1 + 40*x2 <= 3000',
        'x1 <= x2',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_transportation_problem():
    # Create a new model
    model = gp.Model("PeanutTransportation")

    # Define variables
    x1 = model.addVar(name="train_trips", vtype=gp.GRB.INTEGER, lb=0)
    x2 = model.addVar(name="truck_trips", vtype=gp.GRB.INTEGER, lb=0)

    # Objective function: Maximize the total number of packages transported
    model.setObjective(80*x1 + 50*x2, gp.GRB.MAXIMIZE)

    # Cost constraint
    model.addConstr(50*x1 + 40*x2 <= 3000, name="cost_constraint")

    # Trip constraint
    model.addConstr(x1 <= x2, name="trip_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gp.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Train Trips: {x1.varValue}")
        print(f"Truck Trips: {x2.varValue}")
        print(f"Total Packages: {80*x1.varValue + 50*x2.varValue}")
    else:
        print("The model is infeasible.")

solve_transportation_problem()
```