To solve this problem, we first need to translate the natural language description into a symbolic representation. Let's define the variables as follows:

- $x_1$ represents the number of single rooms.
- $x_2$ represents the number of couple's rooms.

The objective function is to maximize profit. Given that a profit of $200 is made on each single room and a profit of $1200 is made on each couple's room, the objective function can be represented as:

Maximize: $200x_1 + 1200x_2$

The constraints are:
1. The cruise ship has at most 800 rooms: $x_1 + x_2 \leq 800$
2. At least 125 rooms are reserved for single rooms: $x_1 \geq 125$
3. A minimum of twice as many passengers prefer to travel as a couple and stay in a couple's room than stay in a single's room. Since each couple's room accommodates 2 passengers and each single room accommodates 1 passenger, this constraint can be represented as: $2x_2 \geq 2x_1$

Now, let's represent the problem symbolically:

```json
{
    'sym_variables': [('x1', 'number of single rooms'), ('x2', 'number of couple\'s rooms')],
    'objective_function': 'Maximize: 200*x1 + 1200*x2',
    'constraints': ['x1 + x2 <= 800', 'x1 >= 125', '2*x2 >= 2*x1']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="single_rooms", vtype=GRB.INTEGER, lb=0)
x2 = m.addVar(name="couple_rooms", vtype=GRB.INTEGER, lb=0)

# Set the objective function
m.setObjective(200*x1 + 1200*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 800, name="total_rooms")
m.addConstr(x1 >= 125, name="single_room_minimum")
m.addConstr(2*x2 >= 2*x1, name="couple_preference")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Single rooms: {x1.x}")
    print(f"Couple's rooms: {x2.x}")
    print(f"Maximum profit: ${200*x1.x + 1200*x2.x}")
else:
    print("No optimal solution found")
```