## Problem Description and Symbolic Representation

The problem involves a banana farmer who needs to transport bananas using cars and motorbikes. The goal is to maximize the number of bananas transported while adhering to certain constraints.

### Symbolic Variables:
- $x_1$ represents the number of cars.
- $x_2$ represents the number of bikes.

### Objective Function:
The objective is to maximize the total number of bananas transported. Each car can take 100 bananas, and each bike can take 30 bananas. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 100x_1 + 30x_2 \]

### Constraints:
1. The cost of running each car is $10, and each bike is $6. The farmer wants to spend at most $200 on transporting bananas. This can be represented as:
\[ 10x_1 + 6x_2 \leq 200 \]
2. The number of cars must be less than the number of bikes:
\[ x_1 < x_2 \]
For practical purposes in linear programming, we can represent this as:
\[ x_1 - x_2 \leq -1 \]
3. Non-negativity constraints, as the number of cars and bikes cannot be negative:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]
And since $x_1$ and $x_2$ represent the number of vehicles, they should also be integers:
\[ x_1 \in \mathbb{Z}, \quad x_2 \in \mathbb{Z} \]
However, for the LP formulation, we first consider them as continuous variables.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'cars'), ('x2', 'bikes')],
    'objective_function': '100*x1 + 30*x2',
    'constraints': [
        '10*x1 + 6*x2 <= 200',
        'x1 - x2 <= -1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="cars", lb=0, vtype=gurobi.GRB.INTEGER)  # Number of cars
    x2 = model.addVar(name="bikes", lb=0, vtype=gurobi.GRB.INTEGER)  # Number of bikes

    # Objective function: Maximize 100*x1 + 30*x2
    model.setObjective(100*x1 + 30*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(10*x1 + 6*x2 <= 200, name="cost_constraint")
    model.addConstr(x1 - x2 <= -1, name="vehicle_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Cars: {x1.varValue}")
        print(f"Bikes: {x2.varValue}")
        print(f"Max Bananas: {100*x1.varValue + 30*x2.varValue}")
    else:
        print("The model is infeasible")

solve_transportation_problem()
```