## Step 1: Define the symbolic representation of the variables
The variables are 'lilies', 'petunias', and 'zucchini vines', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : lilies
- $x_1$ : petunias
- $x_2$ : zucchini vines

## 3: Define the objective function in symbolic notation
The objective function to maximize is $6x_0 + 4x_1 + 5x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $5x_0 + 2x_1 + 3x_2 \leq 122$ (water need)
- $6x_0 + x_1 + 6x_2 \leq 53$ (beauty rating)
- $3x_0 + 7x_1 + 4x_2 \leq 106$ (planting space)
- $7x_1 + 4x_2 \geq 31*144$ (at least 31 square feet of planting space with petunias and zucchini vines, converting to square inches)
- $3x_0 + 7x_1 \geq 25*144$ (lilies and petunias must take up at least 25 ft^2 of planting space, converting to square inches)
- $5x_0 + 3x_2 \leq 97$ (total water need of lilies and zucchini vines)
- $5x_0 + 2x_1 \leq 89$ (total water need of lilies plus petunias)
- $2x_1 + 3x_2 \leq 84$ (total water need of petunias plus zucchini vines)
- $5x_0 + 2x_1 + 3x_2 \leq 85$ (maximum water available for all)
- $6x_0 + x_1 + 6x_2 \leq 25$ (total combined beauty rating from all)
- $x_1 + 6x_2 \leq 25$ (total combined beauty rating from petunias and zucchini vines)
- $6x_0 + 6x_2 \leq 47$ (total combined beauty rating from lilies and zucchini vines)
- $3x_0 + 7x_1 \leq 48*144$ (total planting space occupied by lilies and petunias)
- $3x_0 + 4x_2 \leq 101*144$ (lilies and zucchini vines must take up at most 101 sq. ft of planting space, converting to square inches)
- $3x_0 + 7x_1 + 4x_2 \leq 66*144$ (total planting space occupied by all, converting to square inches)
- $x_0, x_1, x_2 \in \mathbb{Z}$ (integer constraints)

## 5: Create the symbolic representation dictionary
```json
{
    'sym_variables': [('x0', 'lilies'), ('x1', 'petunias'), ('x2', 'zucchini vines')],
    'objective_function': '6*x0 + 4*x1 + 5*x2',
    'constraints': [
        '5*x0 + 2*x1 + 3*x2 <= 122',
        '6*x0 + x1 + 6*x2 <= 53',
        '3*x0 + 7*x1 + 4*x2 <= 106',
        '7*x1 + 4*x2 >= 31*144',
        '3*x0 + 7*x1 >= 25*144',
        '5*x0 + 3*x2 <= 97',
        '5*x0 + 2*x1 <= 89',
        '2*x1 + 3*x2 <= 84',
        '5*x0 + 2*x1 + 3*x2 <= 85',
        '6*x0 + x1 + 6*x2 <= 25',
        'x1 + 6*x2 <= 25',
        '6*x0 + 6*x2 <= 47',
        '3*x0 + 7*x1 <= 48*144',
        '3*x0 + 4*x2 <= 101*144',
        '3*x0 + 7*x1 + 4*x2 <= 66*144'
    ]
}
```

## 6: Write the Gurobi code
```python
import gurobi

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

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

    # Define the objective function
    model.setObjective(6 * lilies + 4 * petunias + 5 * zucchini_vines, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5 * lilies + 2 * petunias + 3 * zucchini_vines <= 122)  # water need
    model.addConstr(6 * lilies + petunias + 6 * zucchini_vines <= 53)  # beauty rating
    model.addConstr(3 * lilies + 7 * petunias + 4 * zucchini_vines <= 106)  # planting space
    model.addConstr(7 * petunias + 4 * zucchini_vines >= 31 * 144)  # at least 31 square feet of planting space with petunias and zucchini vines
    model.addConstr(3 * lilies + 7 * petunias >= 25 * 144)  # lilies and petunias must take up at least 25 ft^2 of planting space
    model.addConstr(5 * lilies + 3 * zucchini_vines <= 97)  # total water need of lilies and zucchini vines
    model.addConstr(5 * lilies + 2 * petunias <= 89)  # total water need of lilies plus petunias
    model.addConstr(2 * petunias + 3 * zucchini_vines <= 84)  # total water need of petunias plus zucchini vines
    model.addConstr(5 * lilies + 2 * petunias + 3 * zucchini_vines <= 85)  # maximum water available for all
    model.addConstr(6 * lilies + petunias + 6 * zucchini_vines <= 25)  # total combined beauty rating from all
    model.addConstr(petunias + 6 * zucchini_vines <= 25)  # total combined beauty rating from petunias and zucchini vines
    model.addConstr(6 * lilies + 6 * zucchini_vines <= 47)  # total combined beauty rating from lilies and zucchini vines
    model.addConstr(3 * lilies + 7 * petunias <= 48 * 144)  # total planting space occupied by lilies and petunias
    model.addConstr(3 * lilies + 4 * zucchini_vines <= 101 * 144)  # lilies and zucchini vines must take up at most 101 sq. ft of planting space
    model.addConstr(3 * lilies + 7 * petunias + 4 * zucchini_vines <= 66 * 144)  # total planting space occupied by all

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objval)
        print("Lilies: ", lilies.varValue)
        print("Petunias: ", petunias.varValue)
        print("Zucchini Vines: ", zucchini_vines.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```