## Problem Description and Symbolic Representation

The problem requires us to maximize the return on investment by allocating $10 million between the energy sector and the travel sector. The energy sector offers a 32% return, while the travel sector offers a 20% return. The constraints are that at least 25% of the investment should be in the energy sector and at most 50% in the travel sector.

## Symbolic Representation

Let's define the symbolic variables:
- $x_1$ : Amount invested in the energy sector
- $x_2$ : Amount invested in the travel sector

The objective function to maximize the total return is: $0.32x_1 + 0.20x_2$

The constraints are:
1. $x_1 + x_2 = 10,000,000$ (Total investment is $10 million)
2. $x_1 \geq 0.25 \times 10,000,000$ (At least 25% in the energy sector)
3. $x_2 \leq 0.50 \times 10,000,000$ (At most 50% in the travel sector)
4. $x_1, x_2 \geq 0$ (Non-negativity constraint)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'Amount invested in the energy sector'), ('x2', 'Amount invested in the travel sector')],
    'objective_function': '0.32*x1 + 0.20*x2',
    'constraints': [
        'x1 + x2 = 10,000,000',
        'x1 >= 0.25 * 10,000,000',
        'x2 <= 0.50 * 10,000,000',
        'x1, x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Investment_Problem")

# Define variables
x1 = model.addVar(name="Energy_Sector", lb=0)  # Amount invested in the energy sector
x2 = model.addVar(name="Travel_Sector", lb=0)  # Amount invested in the travel sector

# Objective function: Maximize 0.32*x1 + 0.20*x2
model.setObjective(0.32 * x1 + 0.20 * x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + x2 == 10000000, name="Total_Investment")  # Total investment is $10 million
model.addConstr(x1 >= 0.25 * 10000000, name="Min_Energy_Sector")  # At least 25% in the energy sector
model.addConstr(x2 <= 0.50 * 10000000, name="Max_Travel_Sector")  # At most 50% in the travel sector

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Amount invested in the energy sector: ${x1.varValue}")
    print(f"Amount invested in the travel sector: ${x2.varValue}")
    print(f"Total return: ${0.32 * x1.varValue + 0.20 * x2.varValue}")
else:
    print("The model is infeasible.")
```