To solve Lucy's investment problem, we need to maximize her profit given the constraints on investing in the automotive and textile industries. Let's denote:

- $x$ as the amount invested in the automotive industry,
- $y$ as the amount invested in the textile industry.

The objective function (profit) can be represented as $0.10x + 0.08y$, since $x$ earns a 10% return and $y$ earns an 8% return.

Given constraints are:
1. The total investment is $30,000: $x + y \leq 30000$
2. The money invested in the automotive industry must be at least three times as much as the money invested in the textile industry: $x \geq 3y$
3. The money invested in the automotive industry must be at most $24,000: $x \leq 24000$
4. Non-negativity constraints: $x \geq 0$ and $y \geq 0$, since investments cannot be negative.

We aim to maximize profit under these conditions.

Here is how we can represent this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="automotive_investment")
y = m.addVar(vtype=GRB.CONTINUOUS, name="textile_investment")

# Objective function: Maximize profit
m.setObjective(0.10*x + 0.08*y, GRB.MAXIMIZE)

# Constraints
m.addConstr(x + y <= 30000, "total_investment")
m.addConstr(x >= 3*y, "automotive_vs_textile")
m.addConstr(x <= 24000, "max_automotive")
m.addConstr(x >= 0, "non_negative_x")
m.addConstr(y >= 0, "non_negative_y")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Automotive Investment: ${x.x:.2f}")
    print(f"Textile Investment: ${y.x:.2f}")
    print(f"Max Profit: ${m.ObjVal:.2f}")
else:
    print("No optimal solution found")
```