To solve the optimization problem described, we first need to define the symbolic representation of the variables and constraints involved. 

The variables are:
- `x0`: The number of boxwoods.
- `x1`: The number of lilies.

Given these variables, the objective function is to minimize: 
9.81*x0 + 3.17*x1

The constraints can be listed as follows:
1. Dollar cost constraint for boxwoods and lilies: 5*x0 + x1 >= 31
2. Water need constraint: 7*x0 + 7*x1 >= 9
3. Another dollar cost constraint (identical to the first but ensuring clarity): 5*x0 + x1 >= 31
4. The total water need should be at least 9 inches per week, which is already covered.
5. Linear constraint: 7*x0 - 2*x1 >= 0
6. Upper bound on dollar cost: 5*x0 + x1 <= 46
7. Upper bound on total water need: 7*x0 + 7*x1 <= 35
8. Integer constraints for both boxwoods and lilies, meaning x0 and x1 must be whole numbers.

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x0', 'boxwoods'), ('x1', 'lilies')],
    'objective_function': '9.81*x0 + 3.17*x1',
    'constraints': [
        '5*x0 + x1 >= 31', 
        '7*x0 + 7*x1 >= 9', 
        '5*x0 + x1 >= 31', 
        '7*x0 - 2*x1 >= 0', 
        '5*x0 + x1 <= 46', 
        '7*x0 + 7*x1 <= 35'
    ]
}
```

To implement this problem in Gurobi, we will use Python as our programming language. Here's how the model would look:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="boxwoods")
x1 = m.addVar(vtype=GRB.INTEGER, name="lilies")

# Objective function: Minimize the total cost
m.setObjective(9.81*x0 + 3.17*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(5*x0 + x1 >= 31, "dollar_cost_lower_bound")
m.addConstr(7*x0 + 7*x1 >= 9, "water_need_lower_bound")
m.addConstr(7*x0 - 2*x1 >= 0, "linear_constraint")
m.addConstr(5*x0 + x1 <= 46, "dollar_cost_upper_bound")
m.addConstr(7*x0 + 7*x1 <= 35, "water_need_upper_bound")

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Boxwoods: {x0.x}")
    print(f"Lilies: {x1.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```