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

Let's define:
- $x_1$ as the amount invested in the solar energy company.
- $x_2$ as the amount invested in the wind energy company.

The objective is to maximize profit, given that each dollar invested in the solar energy company yields a profit of $0.10 and each dollar invested in the wind energy company yields a profit of $0.09. The objective function can be represented as:
\[ \text{Maximize:} \quad 0.10x_1 + 0.09x_2 \]

The constraints are:
1. The total investment is $6000, so $x_1 + x_2 = 6000$.
2. At least 45% of the investment should be in the solar energy company, which translates to $x_1 \geq 0.45 \times 6000$ or $x_1 \geq 2700$.
3. At least $3000 should be invested in the wind energy company, so $x_2 \geq 3000$.

In symbolic notation and natural language description pairs:
- $(x_1, \text{solar energy investment})$
- $(x_2, \text{wind energy investment})$

The objective function with symbolic variables is: $0.10x_1 + 0.09x_2$

The list of constraints where natural language objects are substituted with their symbolic variable counterparts:
- $x_1 + x_2 = 6000$
- $x_1 \geq 2700$
- $x_2 \geq 3000$

Thus, the symbolic representation of the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'solar energy investment'), ('x2', 'wind energy investment')],
    'objective_function': '0.10*x1 + 0.09*x2',
    'constraints': ['x1 + x2 = 6000', 'x1 >= 2700', 'x2 >= 3000']
}
```

Now, let's write the Gurobi code in Python to solve this optimization problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=2700, name="solar_energy_investment")
x2 = m.addVar(lb=3000, name="wind_energy_investment")

# Set the objective function
m.setObjective(0.10*x1 + 0.09*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 == 6000, name="total_investment")
m.update()

# Solve the model
m.optimize()

# Print the solution
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Objective:", m.objVal)
```