Here's our approach to formulating and solving this optimization problem using Gurobi in Python:

**Decision Variables:**

*  `c`: Number of cushioned seats sold.
*  `r`: Number of regular seats sold.

**Objective Function:**

Maximize profit: `30c + 10r`

**Constraints:**

* **Total Seats:** `c + r <= 150` (The bus has a maximum of 150 seats)
* **Minimum Cushioned Seats:** `c >= 50` (At least 50 seats must be cushioned)
* **Regular Seat Preference:** `r >= 2c` (At least twice as many regular seats as cushioned seats are preferred)
* **Non-negativity:** `c >= 0`, `r >= 0` (We cannot sell a negative number of seats)


```python
import gurobipy as gp
from gurobipy import GRB

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

# Create decision variables
c = m.addVar(lb=0, vtype=GRB.INTEGER, name="cushioned_seats")
r = m.addVar(lb=0, vtype=GRB.INTEGER, name="regular_seats")

# Set objective function
m.setObjective(30*c + 10*r, GRB.MAXIMIZE)

# Add constraints
m.addConstr(c + r <= 150, "total_seats")
m.addConstr(c >= 50, "min_cushioned")
m.addConstr(r >= 2*c, "regular_preference")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of cushioned seats: {c.x}")
    print(f"Number of regular seats: {r.x}")
    print(f"Maximum profit: ${m.objVal}")
elif m.status == GRB.INFEASIBLE:
    print("Model is infeasible. No solution found.")
else:
    print(f"Optimization terminated with status: {m.status}")

```
