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

Let's denote:
- \(x_1\) as the amount invested in the healthcare industry,
- \(x_2\) as the amount invested in the energy sector.

The objective is to maximize the return on investment. Given that the healthcare industry yields a 4% return and the energy sector yields an 8% return, the total return can be represented by the objective function:
\[ \text{Maximize: } 0.04x_1 + 0.08x_2 \]

The constraints are as follows:
1. The total investment is $500,000:
\[ x_1 + x_2 \leq 500,000 \]
2. At least 60% of the investment must be in the healthcare industry:
\[ x_1 \geq 0.6 \times 500,000 \]
\[ x_1 \geq 300,000 \]
3. At most 35% of the investment can be in the energy sector:
\[ x_2 \leq 0.35 \times 500,000 \]
\[ x_2 \leq 175,000 \]
4. Non-negativity constraints (since we cannot invest a negative amount):
\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

Now, let's represent the problem symbolically:
```json
{
  'sym_variables': [('x1', 'Amount invested in healthcare industry'), ('x2', 'Amount invested in energy sector')],
  'objective_function': 'Maximize: 0.04*x1 + 0.08*x2',
  'constraints': [
    'x1 + x2 <= 500000',
    'x1 >= 300000',
    'x2 <= 175000',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

To solve this problem using Gurobi in Python, we will use the following code:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(0.04*x1 + 0.08*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 500000, "total_investment")
m.addConstr(x1 >= 300000, "healthcare_minimum")
m.addConstr(x2 <= 175000, "energy_maximum")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Healthcare Investment: {x1.x}")
    print(f"Energy Investment: {x2.x}")
    print(f"Total Return: {0.04*x1.x + 0.08*x2.x}")
else:
    print("No optimal solution found")
```