## Step 1: Define the symbolic representation of the variables
The variables are 'chili plants', 'potato vines', 'pansies', 'basil plants' which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $6 \times (\text{chili plants}) + 3 \times (\text{potato vines}) + 6 \times (\text{pansies}) + 5 \times (\text{basil plants})$. In symbolic notation, this is $6x_0 + 3x_1 + 6x_2 + 5x_3$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $20x_0 + 4x_1 + 20x_2 + 2x_3 \geq 16 \times 144$ (total planting space occupied must be at least 16 ft^2, converting ft^2 to in^2: $1 \text{ ft}^2 = 144 \text{ in}^2$),
2. $20x_0 + 4x_1 \geq 37 \times 144$ (potato vines and chili plants must take up at least 37 ft^2),
3. $20x_0 + 2x_3 \geq 17 \times 144$ (chili plants and basil plants must take up at least 17 ft^2),
4. $20x_2 + 2x_3 \geq 16 \times 144$ (pansies and basil plants must take up at least 16 ft^2),
5. $18x_0 + 7x_1 + 17x_2 + 14x_3 \geq 298$ (total beauty rating),
6. $18x_0 + 17x_2 \geq 65$ (total combined beauty rating from chili plants and pansies),
7. $18x_0 + 14x_3 \geq 63$ (total combined beauty rating from chili plants and basil plants),
8. $18x_0 + 7x_1 + 17x_2 \geq 53$ (total combined beauty rating from chili plants, potato vines, and pansies),
9. $7x_1 + 17x_2 + 14x_3 \geq 53$ (total combined beauty rating from potato vines, pansies, and basil plants),
10. $18x_0 + 7x_1 + 17x_2 \geq 61$ (total combined beauty rating from chili plants, potato vines, and pansies must be 61 or more),
11. $7x_1 + 17x_2 + 14x_3 \geq 61$ (total combined beauty rating from potato vines, pansies, and basil plants must be greater than or equal to 61),
12. $18x_0 + 7x_1 + 17x_2 + 14x_3 \geq 61$ (total combined beauty rating from all must be 61 at minimum),
13. $-10x_0 + 9x_1 \geq 0$,
14. $3x_1 - 10x_2 \geq 0$,
15. $7x_1 + 14x_3 \leq 168$ (total combined beauty rating from potato vines and basil plants),
16. $17x_2 + 14x_3 \leq 230$ (total combined beauty rating from pansies and basil plants),
17. $18x_0 + 17x_2 + 14x_3 \leq 120$ (total combined beauty rating from chili plants, pansies, and basil plants).

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'chili plants'),
        ('x1', 'potato vines'),
        ('x2', 'pansies'),
        ('x3', 'basil plants')
    ],
    'objective_function': '6x0 + 3x1 + 6x2 + 5x3',
    'constraints': [
        '20x0 + 4x1 + 20x2 + 2x3 >= 2304',
        '20x0 + 4x1 >= 5328',
        '20x0 + 2x3 >= 2448',
        '20x2 + 2x3 >= 2304',
        '18x0 + 7x1 + 17x2 + 14x3 >= 298',
        '18x0 + 17x2 >= 65',
        '18x0 + 14x3 >= 63',
        '18x0 + 7x1 + 17x2 >= 53',
        '7x1 + 17x2 + 14x3 >= 53',
        '18x0 + 7x1 + 17x2 >= 61',
        '7x1 + 17x2 + 14x3 >= 61',
        '18x0 + 7x1 + 17x2 + 14x3 >= 61',
        '-10x0 + 9x1 >= 0',
        '3x1 - 10x2 >= 0',
        '7x1 + 14x3 <= 168',
        '17x2 + 14x3 <= 230',
        '18x0 + 17x2 + 14x3 <= 120'
    ]
}
```

## 5: Write the Gurobi code for the optimization problem
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="chili_plants", vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name="potato_vines", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="pansies", vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name="basil_plants", vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(6 * x0 + 3 * x1 + 6 * x2 + 5 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(20 * x0 + 4 * x1 + 20 * x2 + 2 * x3 >= 2304)
    model.addConstr(20 * x0 + 4 * x1 >= 5328)
    model.addConstr(20 * x0 + 2 * x3 >= 2448)
    model.addConstr(20 * x2 + 2 * x3 >= 2304)
    model.addConstr(18 * x0 + 7 * x1 + 17 * x2 + 14 * x3 >= 298)
    model.addConstr(18 * x0 + 17 * x2 >= 65)
    model.addConstr(18 * x0 + 14 * x3 >= 63)
    model.addConstr(18 * x0 + 7 * x1 + 17 * x2 >= 53)
    model.addConstr(7 * x1 + 17 * x2 + 14 * x3 >= 53)
    model.addConstr(18 * x0 + 7 * x1 + 17 * x2 >= 61)
    model.addConstr(7 * x1 + 17 * x2 + 14 * x3 >= 61)
    model.addConstr(18 * x0 + 7 * x1 + 17 * x2 + 14 * x3 >= 61)
    model.addConstr(-10 * x0 + 9 * x1 >= 0)
    model.addConstr(3 * x1 - 10 * x2 >= 0)
    model.addConstr(7 * x1 + 14 * x3 <= 168)
    model.addConstr(17 * x2 + 14 * x3 <= 230)
    model.addConstr(18 * x0 + 17 * x2 + 14 * x3 <= 120)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Chili plants: ", x0.varValue)
        print("Potato vines: ", x1.varValue)
        print("Pansies: ", x2.varValue)
        print("Basil plants: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```