To solve the banana farmer's transportation problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in terms of these variables.

Let's define:
- $x$ as the number of cars used for transportation.
- $y$ as the number of motorcycles (bikes) used for transportation.

The objective is to maximize the total number of bananas transported, which can be represented by the objective function: $100x + 30y$.

Given constraints are:
1. The cost constraint: Each car costs $10 per trip, and each bike costs $6 per trip, with a total budget of $200. This translates to $10x + 6y \leq 200$.
2. The traffic law constraint: The number of cars must be less than the number of bikes, which gives us $x < y$.

However, since we are dealing with linear programming and need to ensure that our constraints can be represented as linear inequalities, we need to consider how to handle the strict inequality $x < y$. For practical purposes in this context, and considering the nature of the variables (which represent counts of cars and bikes), we can interpret this constraint in a way that makes sense for integer values. Since both $x$ and $y$ must be non-negative integers (you cannot have a fraction of a car or bike), we could consider $x \leq y - 1$ as a linearized version that captures the essence of "less than" while avoiding strict inequalities in our formulation.

The symbolic representation of the problem can thus be summarized as follows:

```json
{
    'sym_variables': [('x', 'number of cars'), ('y', 'number of motorcycles (bikes)')],
    'objective_function': 'Maximize 100x + 30y',
    'constraints': [
        '10x + 6y <= 200',  # Cost constraint
        'x <= y - 1'         # Traffic law constraint adjusted for integer values
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(vtype=GRB.INTEGER, name="cars")
y = m.addVar(vtype=GRB.INTEGER, name="motorcycles")

# Set the objective function
m.setObjective(100*x + 30*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x + 6*y <= 200, "cost_constraint")
m.addConstr(x <= y - 1, "traffic_law_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cars: {x.x}")
    print(f"Motorcycles: {y.x}")
    print(f"Total bananas transported: {100*x.x + 30*y.x}")
else:
    print("No optimal solution found")
```