To solve Luke's problem, we first need to translate the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of acres of Danvers carrots.
- $x_2$ as the number of acres of Nantes carrots.

The objective function is to maximize net revenue. The net revenue per acre for Danvers carrots is $600, and for Nantes carrots, it is $300. Thus, the objective function can be written as:

Maximize: $600x_1 + 300x_2$

Now, let's consider the constraints:

1. **Labor Constraint**: Each acre of Danvers carrots requires 2.5 days of labor, and each acre of Nantes carrots requires 3.7 days of labor. Luke has 300 days worth of labor available.
   - $2.5x_1 + 3.7x_2 \leq 300$

2. **Maintenance Costs Constraint**: Each acre of Danvers carrots requires $100 in maintenance costs, and each acre of Nantes carrots requires $200 in maintenance costs. Luke has $20,000 available for maintenance costs.
   - $100x_1 + 200x_2 \leq 20000$

3. **Non-Negativity Constraints**: The number of acres cannot be negative.
   - $x_1 \geq 0$
   - $x_2 \geq 0$

4. **Total Land Constraint**: Luke has a total of 150 acres available for farming.
   - $x_1 + x_2 \leq 150$

The symbolic representation of the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'acres of Danvers carrots'), ('x2', 'acres of Nantes carrots')],
    'objective_function': '600*x1 + 300*x2',
    'constraints': [
        '2.5*x1 + 3.7*x2 <= 300',
        '100*x1 + 200*x2 <= 20000',
        'x1 >= 0',
        'x2 >= 0',
        'x1 + x2 <= 150'
    ]
}
```

Here is the Gurobi code to solve this problem:
```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, name="Danvers_Carrots")
x2 = m.addVar(lb=0, name="Nantes_Carrots")

# Set the objective function
m.setObjective(600*x1 + 300*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2.5*x1 + 3.7*x2 <= 300, "Labor_Constraint")
m.addConstr(100*x1 + 200*x2 <= 20000, "Maintenance_Costs_Constraint")
m.addConstr(x1 + x2 <= 150, "Total_Land_Constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Acres of Danvers carrots: {x1.x}")
    print(f"Acres of Nantes carrots: {x2.x}")
    print(f"Maximum net revenue: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```