To solve this problem, we need to set up a linear programming model that captures the constraints and objectives described. Let's break down the key elements:

1. **Decision Variables**: We have two main decision variables - the number of acres to plant carrots (let's call it `x`) and the number of acres to plant beets (let's call it `y`).

2. **Objective Function**: The farmer wants to maximize profit. Given that the profit per acre of carrots is $500 and the profit per acre of beets is $400, the objective function can be represented as: Maximize `500x + 400y`.

3. **Constraints**:
   - **Land Availability**: The total land available is 30 acres, so `x + y <= 30`.
   - **Minimum Planting Requirements**: There must be a minimum of 3 acres of carrots and 5 acres of beets, so `x >= 3` and `y >= 5`.
   - **Labor Constraints**: The farmer can plant at most twice the quantity of beets as carrots, so `y <= 2x`.

4. **Non-Negativity Constraints**: Since we cannot have negative acres planted, both `x` and `y` must be non-negative.

Now, let's translate these into Gurobi code in Python:

```python
from gurobipy import *

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

# Decision variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="carrots_acres")
y = m.addVar(vtype=GRB.CONTINUOUS, name="beets_acres")

# Objective function: Maximize profit
m.setObjective(500*x + 400*y, GRB.MAXIMIZE)

# Constraints
m.addConstr(x + y <= 30, "land_availability")
m.addConstr(x >= 3, "min_carrots")
m.addConstr(y >= 5, "min_beets")
m.addConstr(y <= 2*x, "labor_constraints")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Carrots acres: {x.x}")
    print(f"Beets acres: {y.x}")
    print(f"Total profit: ${500*x.x + 400*y.x}")
else:
    print("No optimal solution found")
```