To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's define:
- $x_1$ as the number of acres of corn to be grown,
- $x_2$ as the number of acres of wheat to be grown.

The objective is to maximize profit. Given that the profit per acre of corn is $200 and the profit per acre of wheat is $300, the objective function can be written as:
\[ \text{Maximize:} \quad 200x_1 + 300x_2 \]

The constraints based on the problem description are:
1. The farmer has 40 acres of land in total: \( x_1 + x_2 \leq 40 \)
2. He must grow at least 6 acres of corn: \( x_1 \geq 6 \)
3. He must grow at least 12 acres of wheat: \( x_2 \geq 12 \)
4. The amount of corn grown cannot be more than twice the amount of wheat: \( x_1 \leq 2x_2 \)

All variables are non-negative since they represent acres of land.

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'acres of corn'), ('x2', 'acres of wheat')],
    'objective_function': '200*x1 + 300*x2',
    'constraints': ['x1 + x2 <= 40', 'x1 >= 6', 'x2 >= 12', 'x1 <= 2*x2', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="acres_of_corn", lb=0)
x2 = m.addVar(name="acres_of_wheat", lb=0)

# Set the objective function
m.setObjective(200*x1 + 300*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 40, name="total_acres")
m.addConstr(x1 >= 6, name="min_corn")
m.addConstr(x2 >= 12, name="min_wheat")
m.addConstr(x1 <= 2*x2, name="corn_to_wheat_ratio")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Acres of Corn: {x1.x}")
    print(f"Acres of Wheat: {x2.x}")
    print(f"Total Profit: ${200*x1.x + 300*x2.x:.2f}")
else:
    print("No optimal solution found")

```