To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- $x_1$ as the number of acres to plant carrots,
- $x_2$ as the number of acres to plant beets.

The objective is to maximize profit, given that the profit per acre of carrots is $500 and the profit per acre of beets is $400. Thus, the objective function can be represented as:
\[ \text{Maximize:} \quad 500x_1 + 400x_2 \]

Now, let's formulate the constraints based on the given conditions:
1. The farmer has 30 acres available in total.
\[ x_1 + x_2 \leq 30 \]
2. The farmer must grow a minimum of 3 acres of carrots.
\[ x_1 \geq 3 \]
3. The farmer must grow a minimum of 5 acres of beets.
\[ x_2 \geq 5 \]
4. Due to labor constraints, the farmer can only plant at most 2 times the quantity of beets as carrots.
\[ x_2 \leq 2x_1 \]

Additionally, since we cannot have negative acres, both $x_1$ and $x_2$ should be non-negative:
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

However, the condition that $x_1 \geq 0$ is implicitly covered by $x_1 \geq 3$, and similarly, $x_2 \geq 0$ is covered by $x_2 \geq 5$. Therefore, we don't need to explicitly state these non-negativity constraints in our final formulation.

Given this analysis, the symbolic representation of the problem can be summarized as:
```json
{
  'sym_variables': [('x1', 'acres of carrots'), ('x2', 'acres of beets')],
  'objective_function': '500*x1 + 400*x2',
  'constraints': ['x1 + x2 <= 30', 'x1 >= 3', 'x2 >= 5', 'x2 <= 2*x1']
}
```

To solve this problem using Gurobi in Python, we can write the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="carrots", vtype=GRB.CONTINUOUS, lb=3)  # Acres of carrots, minimum 3 acres
x2 = m.addVar(name="beets", vtype=GRB.CONTINUOUS, lb=5)    # Acres of beets, minimum 5 acres

# Set the objective function: Maximize profit
m.setObjective(500*x1 + 400*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 30, name="total_acres")     # Total acres constraint
m.addConstr(x2 <= 2*x1, name="beets_to_carrots")   # Beets to carrots ratio constraint

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found:")
    print(f"Acres of carrots: {x1.x}")
    print(f"Acres of beets: {x2.x}")
    print(f"Maximum profit: ${500*x1.x + 400*x2.x:.2f}")
else:
    print("No optimal solution found.")
```