## Step 1: Define the symbolic representation of the variables
The variables are 'boxwoods' and 'lilies', which can be represented symbolically as 'x1' and 'x2' respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function is to minimize $9.81 \times \text{boxwoods} + 3.17 \times \text{ lilies}$, which translates to $9.81x_1 + 3.17x_2$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. $\text{boxwoods} \geq 0$ and $\text{lilies} \geq 0$ (implied by the problem statement, as they are quantities),
2. $5\text{boxwoods} + 1\text{lilies} \geq 31$,
3. $5\text{boxwoods} + 1\text{lilies} \leq 65$,
4. $7\text{boxwoods} + 7\text{lilies} \geq 9$,
5. $7\text{boxwoods} + 7\text{lilies} \leq 38$,
6. $7\text{boxwoods} - 2\text{lilies} \geq 0$,
7. $\text{boxwoods}$ and $\text{lilies}$ are whole numbers.

## 4: Write down the complete symbolic representation
```json
{
'sym_variables': [('x1', 'boxwoods'), ('x2', 'lilies')],
'objective_function': '9.81*x1 + 3.17*x2',
'constraints': [
    '5*x1 + 1*x2 >= 31',
    '5*x1 + 1*x2 <= 65',
    '7*x1 + 7*x2 >= 9',
    '7*x1 + 7*x2 <= 38',
    '7*x1 - 2*x2 >= 0',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

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

    # Objective function: minimize 9.81 * boxwoods + 3.17 * lilies
    model.setObjective(9.81 * boxwoods + 3.17 * lilies, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5 * boxwoods + lilies >= 31, name="cost_min")
    model.addConstr(5 * boxwoods + lilies <= 65, name="cost_max")
    model.addConstr(7 * boxwoods + 7 * lilies >= 9, name="water_min")
    model.addConstr(7 * boxwoods + 7 * lilies <= 38, name="water_max")
    model.addConstr(7 * boxwoods - 2 * lilies >= 0, name="boxwoods_vs_lilies")

    # 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"Lilies: {lilies.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```