## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of single rooms sold
- $x_2$ as the number of couple's rooms sold

The objective is to maximize profit. The profit made on each single room is $200, and on each couple's room is $1200. Therefore, the objective function can be represented as:
\[ \text{Maximize:} \quad 200x_1 + 1200x_2 \]

## Step 2: Define the constraints

1. The cruise ship has at most 800 rooms:
\[ x_1 + x_2 \leq 800 \]

2. The cruise ship reserves at least 125 rooms 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, this implies:
\[ 2x_2 \geq 2x_1 \]
Simplifying, we get:
\[ x_2 \geq x_1 \]

## 3: Symbolic Representation

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

## 4: Gurobi Code

```python
import gurobipy as gp

# Create a new model
m = gp.Model("CruiseShip")

# Define variables
x1 = m.addVar(name="x1", lb=0, ub=800, vtype=gp.GRB.INTEGER)  # single rooms
x2 = m.addVar(name="x2", lb=0, ub=800, vtype=gp.GRB.INTEGER)  # couple's rooms

# Objective function: Maximize profit
m.setObjective(200*x1 + 1200*x2, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(x1 + x2 <= 800, name="total_rooms")
m.addConstr(x1 >= 125, name="min_single_rooms")
m.addConstr(x2 >= x1, name="couple_to_single_ratio")

# Solve the model
m.optimize()

# Print solution
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
    print(f"Maximum profit: ${200*x1.varValue + 1200*x2.varValue}")
else:
    print("No optimal solution found")
```