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

Let's denote the investment in the healthcare industry as \(x_1\) and the investment in the energy sector as \(x_2\). The objective is to maximize the return on investment, which can be represented as \(0.04x_1 + 0.08x_2\), given that the total investment is $500,000.

## Step 2: Translate natural language into symbolic notation and algebraic terms

- The total investment is $500,000: \(x_1 + x_2 \leq 500,000\)
- At least 60% of the investment should be in the healthcare industry: \(x_1 \geq 0.6 \times 500,000\)
- At most 35% of the investment should be in the energy sector: \(x_2 \leq 0.35 \times 500,000\)
- Non-negativity constraints: \(x_1 \geq 0, x_2 \geq 0\)

## 3: Express the problem in a standard optimization format

### Symbolic Variables:
- \(x_1\) represents the investment in the healthcare industry
- \(x_2\) represents the investment in the energy sector

### Objective Function:
Maximize \(0.04x_1 + 0.08x_2\)

### Constraints:
1. \(x_1 + x_2 \leq 500,000\)
2. \(x_1 \geq 0.6 \times 500,000\)
3. \(x_2 \leq 0.35 \times 500,000\)
4. \(x_1 \geq 0\)
5. \(x_2 \geq 0\)

## 4: Convert the problem into a JSON representation

```json
{
'sym_variables': [('x1', 'healthcare investment'), ('x2', 'energy sector investment')],
'objective_function': '0.04*x1 + 0.08*x2',
'constraints': [
    'x1 + x2 <= 500000',
    'x1 >= 0.6 * 500000',
    'x2 <= 0.35 * 500000',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Implement the problem using Gurobi in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="healthcare_investment", lb=0)
    x2 = model.addVar(name="energy_sector_investment", lb=0)

    # Objective function: Maximize 0.04*x1 + 0.08*x2
    model.setObjective(0.04 * x1 + 0.08 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 500000)
    model.addConstr(x1 >= 0.6 * 500000)
    model.addConstr(x2 <= 0.35 * 500000)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal investment in healthcare: $", x1.varValue)
        print("Optimal investment in energy sector: $", x2.varValue)
        print("Maximum return: ", 0.04 * x1.varValue + 0.08 * x2.varValue)
    else:
        print("The model is infeasible")

solve_investment_problem()
```