To solve Miles's investment problem, we need to formulate a linear programming (LP) model. The goal is to maximize the profit from investing in the floral and healthcare industries under given constraints.

### Symbolic Representation of the Problem:

Let's define the symbolic variables as follows:
- $x_1$: Amount invested in the floral industry.
- $x_2$: Amount invested in the healthcare industry.

The objective function, which represents the total profit Miles wants to maximize, can be written as:
\[ \text{Maximize:} \quad 1.3x_1 + 1.5x_2 \]

The constraints based on the problem description are:
1. The total amount invested cannot exceed $10,000: \( x_1 + x_2 \leq 10000 \).
2. At least 25% of all the money invested must be in the floral industry: \( x_1 \geq 0.25(x_1 + x_2) \).
3. At least $2000 must be invested in the healthcare industry: \( x_2 \geq 2000 \).
4. Non-negativity constraints, as the amount invested cannot be negative: \( x_1 \geq 0, x_2 \geq 0 \).

### JSON Representation:
```json
{
    'sym_variables': [('x1', 'Amount invested in the floral industry'), ('x2', 'Amount invested in the healthcare industry')],
    'objective_function': 'Maximize: 1.3*x1 + 1.5*x2',
    'constraints': [
        'x1 + x2 <= 10000',
        'x1 >= 0.25*(x1 + x2)',
        'x2 >= 2000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

### Gurobi Code in Python:
```python
from gurobipy import *

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

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

# Objective function: Maximize profit
m.setObjective(1.3*x1 + 1.5*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(x1 + x2 <= 10000, "Total_Investment")
m.addConstr(x1 >= 0.25*(x1 + x2), "Floral_Industry_Minimum")
m.addConstr(x2 >= 2000, "Healthcare_Industry_Minimum")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Amount invested in Floral Industry: {x1.x}")
    print(f"Amount invested in Healthcare Industry: {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```