## Problem Description and Formulation

The problem is an optimization problem with integer variables, subject to various constraints. The goal is to maximize the objective function:

\[ 8.66 \times \text{boxwoods} + 8.39 \times \text{roses} + 3.72 \times \text{begonias} \]

subject to constraints on planting space and resilience index.

## Constraints

1. Planting space requirements and resilience indices for each plant type are given.
2. Minimum and maximum usage of planting space by different combinations of plants.
3. Minimum and maximum total resilience indices for different combinations of plants.
4. Integer requirements for the number of each plant type.

## Conversion to Gurobi Code

```python
import gurobi

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

    # Define variables
    boxwoods = model.addVar(name="boxwoods", vtype=gurobi.GRB.INTEGER)
    roses = model.addVar(name="roses", vtype=gurobi.GRB.INTEGER)
    begonias = model.addVar(name="begonias", vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(8.66 * boxwoods + 8.39 * roses + 3.72 * begonias, gurobi.GRB.MAXIMIZE)

    # Constraints
    # Planting space constraints
    model.addConstr(8.65 * boxwoods + 1.12 * roses + 0.8 * begonias >= 28 * 144)  # At least 28 sq. ft.
    model.addConstr(8.65 * boxwoods + 0.8 * begonias <= 135 * 144)  # Boxwoods and begonias at most 135 sq. ft.
    model.addConstr(1.12 * roses + 0.8 * begonias <= 68 * 144)  # Roses and begonias at most 68 sq. ft.
    model.addConstr(8.65 * boxwoods + 1.12 * roses <= 128 * 144)  # Boxwoods and roses at most 128 sq. ft.
    model.addConstr(8.65 * boxwoods + 1.12 * roses + 0.8 * begonias <= 67 * 144)  # All plants at most 67 sq. ft.

    # Resilience index constraints
    model.addConstr(9.06 * boxwoods + 5.81 * begonias >= 32)  # Boxwoods and begonias minimum 32
    model.addConstr(6.61 * roses + 5.81 * begonias >= 18)  # Roses and begonias minimum 18
    model.addConstr(9.06 * boxwoods + 6.61 * roses + 5.81 * begonias >= 20)  # All plants minimum 20
    model.addConstr(6.61 * roses + 5.81 * begonias <= 94)  # Roses and begonias maximum 94
    model.addConstr(9.06 * boxwoods + 6.61 * roses <= 35)  # Boxwoods and roses maximum 35
    model.addConstr(9.06 * boxwoods + 6.61 * roses + 5.81 * begonias <= 35)  # All plants maximum 35

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Boxwoods: {boxwoods.varValue}")
        print(f"Roses: {roses.varValue}")
        print(f"Begonias: {begonias.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```