## Problem Description and Formulation

The city has $200,000 available for investment in two industries: film and healthcare, with a 9-month commitment. The goal is to maximize the return on investment (ROI) under the following constraints:

1. The total investment is $200,000.
2. At least 25% of the investment must be in the film industry.
3. At most 60% of the investment can be in the healthcare industry.
4. The film industry yields an 8% return over the 9-month period.
5. The healthcare industry yields a 10% return over the 9-month period.

## Symbolic Representation

Let's denote:
- \(x\) as the amount invested in the film industry.
- \(y\) as the amount invested in the healthcare industry.

The objective function to maximize the total return on investment is:
\[ \text{Maximize:} \quad 0.08x + 0.10y \]

Subject to:
1. \( x + y = 200,000 \) (total investment constraint)
2. \( x \geq 0.25 \times 200,000 \) (minimum film industry investment constraint)
3. \( y \leq 0.60 \times 200,000 \) (maximum healthcare industry investment constraint)
4. \( x, y \geq 0 \) (non-negativity constraint)

## Converting to Gurobi Code

```python
import gurobi

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

    # Define variables
    x = model.addVar(name="film_investment", lb=0)
    y = model.addVar(name="healthcare_investment", lb=0)

    # Objective function: Maximize 0.08x + 0.10y
    model.setObjective(0.08 * x + 0.10 * y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x + y == 200000, name="total_investment")
    model.addConstr(x >= 0.25 * 200000, name="min_film_investment")
    model.addConstr(y <= 0.60 * 200000, name="max_healthcare_investment")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal film investment: ${x.varValue}")
        print(f"Optimal healthcare investment: ${y.varValue}")
        print(f"Max return: ${0.08 * x.varValue + 0.10 * y.varValue}")
    else:
        print("No optimal solution found.")

solve_investment_problem()
```