## Step 1: Define the symbolic representation of the problem

Let's define the symbolic variables:
- $x_1$ = amount invested in the solar energy company
- $x_2$ = amount invested in the wind energy company

The objective function to maximize profit is: $0.10x_1 + 0.09x_2$

The constraints are:
1. Total investment: $x_1 + x_2 \leq 6000$
2. Minimum investment in solar energy: $x_1 \geq 0.45(x_1 + x_2)$
3. Minimum investment in wind energy: $x_2 \geq 3000$
4. Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Step 2: Convert the constraints into standard form

1. Total investment: $x_1 + x_2 \leq 6000$
2. Minimum investment in solar energy: $x_1 \geq 0.45x_1 + 0.45x_2$ which simplifies to $0.55x_1 - 0.45x_2 \geq 0$
3. Minimum investment in wind energy: $x_2 \geq 3000$

## 3: Express the problem in the required JSON format

```json
{
    'sym_variables': [('x1', 'amount invested in solar energy company'), ('x2', 'amount invested in wind energy company')],
    'objective_function': '0.10*x1 + 0.09*x2',
    'constraints': [
        'x1 + x2 <= 6000',
        '0.55*x1 - 0.45*x2 >= 0',
        'x2 >= 3000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 4: Implement the problem in Gurobi code

```python
import gurobi

def solve_investment_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="solar_investment", lb=0)
    x2 = model.addVar(name="wind_investment", lb=0)

    # Objective function: maximize 0.10*x1 + 0.09*x2
    model.setObjective(0.10 * x1 + 0.09 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 6000, name="total_investment")
    model.addConstr(0.55 * x1 - 0.45 * x2 >= 0, name="solar_minimum")
    model.addConstr(x2 >= 3000, name="wind_minimum")

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal investment in solar energy company: ", x1.varValue)
        print("Optimal investment in wind energy company: ", x2.varValue)
        print("Maximum profit: ", model.objVal)
    else:
        print("The model is infeasible")

solve_investment_problem()
```