Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Number of premium tickets sold
* `y`: Number of regular tickets sold

**Objective Function:**

Maximize profit: `50x + 30y`

**Constraints:**

* **Capacity Constraint:** `x + y <= 250`  (The Ferris wheel can hold at most 250 people)
* **Minimum Premium Tickets:** `x >= 50` (At least 50 premium tickets must be sold)
* **Regular Ticket Preference:** `y >= 3x` (At least 3 times more regular tickets than premium tickets)
* **Non-negativity:** `x >= 0`, `y >= 0` (Cannot sell negative tickets)


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

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

# Create decision variables
x = model.addVar(lb=0, vtype=GRB.INTEGER, name="premium_tickets") # Integer number of premium tickets
y = model.addVar(lb=0, vtype=GRB.INTEGER, name="regular_tickets") # Integer number of regular tickets


# Set objective function
model.setObjective(50*x + 30*y, GRB.MAXIMIZE)

# Add constraints
model.addConstr(x + y <= 250, "capacity")
model.addConstr(x >= 50, "min_premium")
model.addConstr(y >= 3*x, "regular_preference")


# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Profit: ${model.objVal}")
    print(f"Premium Tickets: {x.x}")
    print(f"Regular Tickets: {y.x}")
elif model.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
