To solve this problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of long-term cruise tickets sold
- $x_2$ as the number of week-long cruise tickets sold

The objective function is to maximize profit, which can be represented algebraically as $500x_1 + 150x_2$, since each long-term ticket brings in $500 and each week-long ticket brings in $150.

The constraints based on the problem description are:

1. The total number of people (from both types of tickets) cannot exceed 1500: $x_1 + x_2 \leq 1500$
2. There must be at least 35 long-term cruise tickets sold: $x_1 \geq 35$
3. At least 4 times as many people prefer to buy week-long cruise tickets than long-term cruise tickets: $x_2 \geq 4x_1$

Therefore, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of long-term cruise tickets sold'), ('x2', 'number of week-long cruise tickets sold')],
    'objective_function': '500*x1 + 150*x2',
    'constraints': ['x1 + x2 <= 1500', 'x1 >= 35', 'x2 >= 4*x1', 'x1 >= 0', 'x2 >= 0']
}
```

Note: We also include non-negativity constraints ($x_1 \geq 0$, $x_2 \geq 0$) because the number of tickets sold cannot be negative.

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="long_term_tickets")
x2 = m.addVar(vtype=GRB.INTEGER, name="week_long_tickets")

# Set the objective function
m.setObjective(500*x1 + 150*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 1500, "total_people")
m.addConstr(x1 >= 35, "min_long_term")
m.addConstr(x2 >= 4*x1, "week_long_preference")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Long-term tickets: {x1.x}")
    print(f"Week-long tickets: {x2.x}")
    print(f"Maximum profit: ${500*x1.x + 150*x2.x}")
else:
    print("No optimal solution found")
```