To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- \(x_1\) as the number of first-floor seats.
- \(x_2\) as the number of second-floor seats.

The objective is to maximize profit, with each first-floor seat making a profit of $100 and each second-floor seat making a profit of $70. Thus, the objective function can be represented as:
\[ \text{Maximize:} \quad 100x_1 + 70x_2 \]

The constraints given are:
1. The total number of seats is 250, so \(x_1 + x_2 = 250\).
2. At least 70 seats must be assigned as first-floor seats, so \(x_1 \geq 70\).
3. At least twice as many people prefer the second-floor seats to the first-floor seats, which can be interpreted as \(x_2 \geq 2x_1\).

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of first-floor seats'), ('x2', 'number of second-floor seats')],
    'objective_function': '100*x1 + 70*x2',
    'constraints': ['x1 + x2 = 250', 'x1 >= 70', 'x2 >= 2*x1']
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(100*x1 + 70*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 == 250, "total_seats")
m.addConstr(x1 >= 70, "first_floor_min")
m.addConstr(x2 >= 2*x1, "second_floor_preference")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"First-floor seats: {x1.x}")
    print(f"Second-floor seats: {x2.x}")
    print(f"Maximum profit: ${100*x1.x + 70*x2.x}")
else:
    print("No optimal solution found")
```