## Problem Description and Formulation

The problem is a linear programming optimization problem. Luke, a carrot farmer, has 150 acres of land to grow two types of carrots: Danvers and Nantes. The goal is to maximize the net revenue given the constraints on labor and maintenance costs.

### Variables
- Let \(D\) be the number of acres of Danvers carrots.
- Let \(N\) be the number of acres of Nantes carrots.

### Objective Function
The net revenue per acre of Danvers carrots is $600, and per acre of Nantes carrots is $300. The objective is to maximize the total net revenue:
\[ \text{Maximize:} \quad 600D + 300N \]

### Constraints
1. **Land Constraint:** Luke has 150 acres of land available.
\[ D + N \leq 150 \]

2. **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 of labor available.
\[ 2.5D + 3.7N \leq 300 \]

3. **Maintenance Cost Constraint:** Each acre of Danvers carrots requires $100 in maintenance costs, and each acre of Nantes carrots requires $200. Luke has $20,000 available for maintenance.
\[ 100D + 200N \leq 20000 \]

4. **Non-Negativity Constraints:** The number of acres cannot be negative.
\[ D \geq 0, N \geq 0 \]

## Gurobi Code

```python
import gurobi

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

    # Define variables
    D = model.addVar(lb=0, name="Danvers_acres")
    N = model.addVar(lb=0, name="Nantes_acres")

    # Objective function: Maximize net revenue
    model.setObjective(600*D + 300*N, gurobi.GRB.MAXIMIZE)

    # Land constraint
    model.addConstr(D + N <= 150, name="Land_constraint")

    # Labor constraint
    model.addConstr(2.5*D + 3.7*N <= 300, name="Labor_constraint")

    # Maintenance cost constraint
    model.addConstr(100*D + 200*N <= 20000, name="Maintenance_cost_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal acres of Danvers carrots: {D.varValue}")
        print(f"Optimal acres of Nantes carrots: {N.varValue}")
        print(f"Maximum net revenue: ${model.objVal:.2f}")
    else:
        print("The problem is infeasible.")

solve_carrot_farming_problem()
```