To solve Luke's problem, we need to maximize the net revenue from growing Danvers and Nantes carrots on his 150 acres of land. The decision variables are the number of acres dedicated to each type of carrot.

Let's denote:
- \(D\) as the number of acres for Danvers carrots,
- \(N\) as the number of acres for Nantes carrots.

The objective function, which is the total net revenue, can be represented as:
\[600D + 300N\]

Given constraints are:
1. Total land: \(D + N \leq 150\)
2. Labor constraint: \(2.5D + 3.7N \leq 300\)
3. Maintenance cost constraint: \(100D + 200N \leq 20000\)
4. Non-negativity constraints: \(D \geq 0, N \geq 0\)

Now, let's write the Gurobi code to solve this linear programming problem:

```python
from gurobipy import *

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

# Define the variables
D = m.addVar(lb=0, name="Danvers")
N = m.addVar(lb=0, name="Nantes")

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

# Add constraints
m.addConstr(D + N <= 150, "Total_Land")
m.addConstr(2.5*D + 3.7*N <= 300, "Labor_Constraint")
m.addConstr(100*D + 200*N <= 20000, "Maintenance_Cost")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal Solution Found:")
    print(f"Acres of Danvers Carrots: {D.x}")
    print(f"Acres of Nantes Carrots: {N.x}")
    print(f"Total Net Revenue: ${m.objVal:.2f}")
else:
    print("No optimal solution found. The model is likely infeasible.")
```