## Problem Description and Formulation

The boat company wants to maximize its profit by selling tickets for vehicles and passengers. The profit for each vehicle ticket is $130, and for each passenger ticket is $60. There are several constraints:

1. The company can sell at most 200 tickets in total.
2. A minimum of 20 tickets must be reserved for vehicles.
3. At least 4 times as many tickets are sold for passengers than for vehicles.

Let's denote the number of vehicle tickets as \(V\) and the number of passenger tickets as \(P\).

## Mathematical Formulation

The objective is to maximize the total profit:
\[ \text{Maximize:} \quad 130V + 60P \]

Subject to the constraints:
1. \( V + P \leq 200 \) (Total tickets constraint)
2. \( V \geq 20 \) (Minimum vehicle tickets constraint)
3. \( P \geq 4V \) (Passenger tickets vs vehicle tickets constraint)
4. \( V \geq 0 \) and \( P \geq 0 \) (Non-negativity constraints)

## Gurobi Code

```python
import gurobi

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

    # Define variables
    V = model.addVar(lb=0, name="Vehicles")
    P = model.addVar(lb=0, name="Passengers")

    # Objective function: Maximize profit
    model.setObjective(130 * V + 60 * P, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(V + P <= 200, name="Total_Tickets")
    model.addConstr(V >= 20, name="Min_Vehicles")
    model.addConstr(P >= 4 * V, name="Passengers_vs_Vehicles")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution found. Vehicles: {V.varValue}, Passengers: {P.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_boat_company_problem()
```

This code defines a Gurobi model for the given problem, sets up the objective function and constraints, and then solves the optimization problem. If an optimal solution is found, it prints out the number of vehicle and passenger tickets to sell and the maximum achievable profit.