Here's our approach to formulating and solving this linear program:

**Decision Variables:**

*  `x`: Number of first-class tickets sold.
*  `y`: Number of economy-class tickets sold.

**Objective Function:**

Maximize profit: `150x + 350y`

**Constraints:**

* **Total Tickets:** `x + y <= 150`
* **Minimum First-Class:** `x >= 20`
* **Economy vs. First-Class Ratio:** `y >= 3x`

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

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

# Create variables
x = m.addVar(vtype=GRB.INTEGER, name="first_class")
y = m.addVar(vtype=GRB.INTEGER, name="economy_class")

# Set objective
m.setObjective(150*x + 350*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x + y <= 150, "total_tickets")
m.addConstr(x >= 20, "min_first_class")
m.addConstr(y >= 3*x, "economy_ratio")

# Optimize model
m.optimize()

if m.status == GRB.OPTIMAL:
    print(f"Optimal Profit: ${m.objVal}")
    print(f"First-Class Tickets: {x.x}")
    print(f"Economy-Class Tickets: {y.x}")
elif m.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
