## Problem Description and Formulation

The problem is a linear programming (LP) optimization problem. Miles wants to invest up to $10,000 in the floral and healthcare industries. He has two main constraints:

1. At least 25% of all the money invested must be in the floral industry.
2. At least $2000 must be invested in the healthcare industry.

The profit from each dollar invested in the floral industry is $1.3, and in the healthcare industry is $1.5. The goal is to maximize Miles's investment.

## Mathematical Formulation

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

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 1.3x + 1.5y \]

Subject to:
1. Total investment constraint: \( x + y \leq 10000 \)
2. Floral industry investment constraint: \( x \geq 0.25(x + y) \)
3. Healthcare industry investment constraint: \( y \geq 2000 \)
4. Non-negativity constraints: \( x \geq 0, y \geq 0 \)

## Simplifying Constraints

The floral industry investment constraint can be simplified:
\[ x \geq 0.25x + 0.25y \]
\[ 0.75x \geq 0.25y \]
\[ 3x \geq y \]

## Gurobi Code

```python
import gurobi

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

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

    # Objective function: Maximize 1.3x + 1.5y
    model.setObjective(1.3 * x + 1.5 * y, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x + y <= 10000, name="total_investment")
    model.addConstr(y >= 2000, name="healthcare_min_investment")
    model.addConstr(3 * x >= y, name="floral_min_investment_ratio")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal investment in floral industry: ${x.varValue}")
        print(f"Optimal investment in healthcare industry: ${y.varValue}")
        print(f"Maximal profit: ${model.objVal}")
    else:
        print("The problem is infeasible.")

solve_investment_problem()
```