## Problem Description and Formulation

The problem is a linear programming (LP) optimization problem. The goal is to maximize the number of potatoes that can be transported given certain constraints.

### Variables
- Let \(T\) be the number of trucks used.
- Let \(V\) be the number of vans used.

### Objective Function
The objective is to maximize the total number of potatoes transported. Each truck can take 150 potatoes, and each van can take 80 potatoes. Therefore, the objective function can be written as:
\[ \text{Maximize:} \quad 150T + 80V \]

### Constraints
1. **Cost Constraint:** The cost of running each truck is $20 per trip, and the cost of running each van is $12 per trip. Bob wants to spend at most $250 on transporting his potatoes. This can be written as:
\[ 20T + 12V \leq 250 \]

2. **Traffic Law Constraint:** The number of trucks must be less than the number of vans.
\[ T < V \]

3. **Non-Negativity Constraint:** The number of trucks and vans cannot be negative.
\[ T \geq 0, \quad V \geq 0 \]

4. **Integer Constraint:** Since we cannot have a fraction of a truck or van, \(T\) and \(V\) should be integers. However, for the LP formulation, we first consider them as continuous variables and then round if necessary.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    T = model.addVar(lb=0, name="Trucks")  # Number of trucks
    V = model.addVar(lb=0, name="Vans")   # Number of vans

    # Objective function: Maximize the number of potatoes transported
    model.setObjective(150*T + 80*V, gurobi.GRB.MAXIMIZE)

    # Cost constraint: 20T + 12V <= 250
    model.addConstr(20*T + 12*V <= 250, name="Cost_Constraint")

    # Traffic law constraint: T < V
    model.addConstr(T <= V - 1, name="Traffic_Law_Constraint")  # Adjusted for integer solution

    # Solve the model
    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: Trucks = {T.varValue}, Vans = {V.varValue}")
        print(f"Max Potatoes Transported: {150*T.varValue + 80*V.varValue}")
    else:
        print("The model is infeasible.")

solve_potato_transportation()
```

This code defines the LP problem using Gurobi's Python interface, sets up the objective function and constraints, and solves the model. Note that for the traffic law constraint \(T < V\), we adjust it to \(T \leq V - 1\) to ensure an integer solution space, as Gurobi solves LP problems and may return fractional values for \(T\) and \(V\). However, in this specific formulation, we keep it as is because Gurobi can handle the strict inequality by adjusting it slightly for practical purposes. The solution will provide the maximum number of potatoes that can be transported under the given conditions.