Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `x`: Acres of carrots planted
* `y`: Acres of beets planted

**Objective Function:**

Maximize profit: `500x + 400y`

**Constraints:**

* **Land Constraint:** `x + y <= 30` (Total acres available)
* **Minimum Carrots:** `x >= 3`
* **Minimum Beets:** `y >= 5`
* **Beets Preference (Beets >= Carrots):** `y >= x`
* **Labor Constraint:** `y <= 2x` (Beets planted at most twice carrots)
* **Non-negativity:** `x >= 0`, `y >= 0`


```python
import gurobipy as gp

# Create a new model
m = gp.Model("farm_optimization")

# Create variables
x = m.addVar(name="carrots", lb=0)  # Acres of carrots
y = m.addVar(name="beets", lb=0)  # Acres of beets

# Set objective function
m.setObjective(500*x + 400*y, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(x + y <= 30, "land_constraint")
m.addConstr(x >= 3, "min_carrots")
m.addConstr(y >= 5, "min_beets")
m.addConstr(y >= x, "beet_preference")
m.addConstr(y <= 2*x, "labor_constraint")


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Plant {x.x:.2f} acres of carrots")
    print(f"Plant {y.x:.2f} acres of beets")
    print(f"Maximum Profit: ${m.objVal:.2f}")
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
