## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the acres of Danvers carrots
- $x_2$ represents the acres of Nantes carrots

## Step 2: Formulate the objective function
The net revenue per acre of Danvers carrots is $600 and the net revenue per acre of Nantes carrots is $300. The objective is to maximize the total net revenue, which can be represented as:
\[ \text{Maximize:} \quad 600x_1 + 300x_2 \]

## 3: Define the constraints
1. **Land constraint**: Luke has 150 acres of land available.
\[ x_1 + x_2 \leq 150 \]
2. **Labor constraint**: Each acre of Danvers carrots requires 2.5 days worth of labor and each acre of Nantes carrots requires 3.7 days worth of labor. Luke has 300 days worth of labor available.
\[ 2.5x_1 + 3.7x_2 \leq 300 \]
3. **Maintenance cost 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.
\[ 100x_1 + 200x_2 \leq 20000 \]
4. **Non-negativity constraint**: The acres of carrots cannot be negative.
\[ x_1 \geq 0, x_2 \geq 0 \]

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

## 5: Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    m = gurobi.Model()

    # Define the variables
    x1 = m.addVar(name="Danvers_carrots", lb=0)
    x2 = m.addVar(name="Nantes_carrots", lb=0)

    # Objective function
    m.setObjective(600 * x1 + 300 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    m.addConstr(x1 + x2 <= 150, name="land_constraint")
    m.addConstr(2.5 * x1 + 3.7 * x2 <= 300, name="labor_constraint")
    m.addConstr(100 * x1 + 200 * x2 <= 20000, name="maintenance_constraint")

    # Optimize the model
    m.optimize()

    # Print the solution
    if m.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Acres of Danvers carrots: {x1.varValue}")
        print(f"Acres of Nantes carrots: {x2.varValue}")
        print(f"Max revenue: {m.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```