## Problem Description and Formulation

The retired teacher has $300,000 to invest in four industries: energy, telecom, utilities, and health care, with annual rates of return of 5%, 8%, 3%, and 9%, respectively. The financial advisor has provided the following constraints:

1. The amount invested in the health care industry cannot exceed the amount invested in the energy industry.
2. The amount invested in the telecom industry cannot exceed the amount invested in the utilities industry.
3. At most 33% of the total amount of money can be invested in the health care industry.

The goal is to maximize the return on investment.

## Symbolic Representation

Let's denote the amount invested in each industry as:

* $E$: energy
* $T$: telecom
* $U$: utilities
* $H$: health care

The objective function to maximize the return on investment is:

$$\max 0.05E + 0.08T + 0.03U + 0.09H$$

Subject to the constraints:

1. $H \leq E$
2. $T \leq U$
3. $H \leq 0.33 \times 300,000$
4. $E + T + U + H \leq 300,000$
5. $E, T, U, H \geq 0$

## Gurobi Code

```python
import gurobi

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

    # Define the variables
    E = model.addVar(lb=0, name="Energy")
    T = model.addVar(lb=0, name="Telecom")
    U = model.addVar(lb=0, name="Utilities")
    H = model.addVar(lb=0, name="Health Care")

    # Objective function: maximize return on investment
    model.setObjective(0.05 * E + 0.08 * T + 0.03 * U + 0.09 * H, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(H <= E, name="Health Care <= Energy")
    model.addConstr(T <= U, name="Telecom <= Utilities")
    model.addConstr(H <= 0.33 * 300000, name="Health Care <= 33% of total")
    model.addConstr(E + T + U + H <= 300000, name="Total investment <= $300,000")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Energy: ${E.varValue:.2f}")
        print(f"Telecom: ${T.varValue:.2f}")
        print(f"Utilities: ${U.varValue:.2f}")
        print(f"Health Care: ${H.varValue:.2f}")
        print(f"Return on investment: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_investment_problem()
```