To solve the given problem, we first need to define the decision variables and the objective function. Let's denote:

- \(x\) as the number of cars used,
- \(y\) as the number of bikes used.

The objective is to maximize the total number of bananas transported. Since each car can take 100 bananas and each bike can take 30 bananas, the total number of bananas transported can be represented by \(100x + 30y\).

We have two main constraints:

1. The cost constraint: The farmer wants to spend at most $200 on transporting his bananas. Given that the cost of running each car is $10 per trip and the cost of running each bike is $6 per trip, this constraint can be represented as \(10x + 6y \leq 200\).

2. The traffic law constraint: The number of cars must be less than the number of bikes, which can be represented as \(x < y\). However, since we are dealing with integer numbers of vehicles and to make this inequality workable in a linear programming context where all variables are typically non-negative, we need to ensure that \(y \geq x + 1\) (since both \(x\) and \(y\) must be integers).

Additionally, both \(x\) and \(y\) should be non-negative integers because you cannot use a negative number of cars or bikes.

Now, let's write the Gurobi code for this problem:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(vtype=GRB.INTEGER, name="cars", lb=0)
y = m.addVar(vtype=GRB.INTEGER, name="bikes", lb=0)

# Set the objective function: Maximize the total number of bananas transported
m.setObjective(100*x + 30*y, GRB.MAXIMIZE)

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

# Optimize model
m.optimize()

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