## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'pansies', 'verbenas', 'potato vines', and 'aloe vera', which we can denote as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $8x_0^2 + 2x_0x_1 + 2x_0x_2 + x_0x_3 + 8x_1^2 + 4x_1x_2 + 8x_1x_3 + 2x_2^2 + x_2x_3 + 6x_3^2 + 4x_0 + 2x_1 + 4x_2 + 2x_3$.

## 3: List the constraints in symbolic notation
1. $x_0 \geq 0$ and $x_0$ is an integer (nonfractional number of pansies)
2. $x_1 \geq 0$ and $x_1$ is an integer (nonfractional number of verbenas)
3. $x_2 \geq 0$ and $x_2$ is an integer (nonfractional number of potato vines)
4. $x_3 \geq 0$ and $x_3$ is an integer (nonfractional number of aloe vera)
5. $5x_0 + 11x_1 + 10x_2 + 6x_3 \leq 73$ (resilience index)
6. $2x_0 + 9x_1 + 9x_2 + 7x_3 \leq 73$ (planting space)
7. $3x_0 + 9x_1 + x_2 + 11x_3 \leq 200$ (dollar cost)
8. $2x_0 + 9x_1 + 9x_2 \geq 17 \times 144$ (at least 17 sq. ft of planting space on pansies and potato vines)
9. $9x_1 + 9x_2 \geq 17 \times 144$ (at least 17 sq. ft of planting space on verbenas and potato vines)
10. $2x_0 + 9x_2 + 7x_3 \geq 16 \times 144$ (at least 16 sq. ft of planting space with pansies, potato vines, and aloe vera)
11. $2x_0 + 9x_1 + 7x_3 \geq 16 \times 144$ (total planting space occupied by pansies, verbenas, and aloe vera)
12. $2^2x_0^2 + 9^2x_2^2 + 7^2x_3^2 \geq 10 \times 144$ (total planting space occupied by pansies, potato vines, and aloe vera squared)
13. $2x_0 + 9x_1 + 7x_3 \geq 10 \times 144$ (at least 10 sq. ft of planting space with pansies, verbenas, and aloe vera)
14. $3x_0 + x_2 \geq 22$ (at least $22 on pansies and potato vines)
15. $3x_0 + 9x_1 + x_2 \geq 35$ (at least $35 on pansies, verbenas, and potato vines)
16. $6x_0 - 4x_1 + x_2 \geq 0$ (linear constraint)
17. $10x_2 + 6x_3 \leq 28$ (resilience index from potato vines and aloe vera)
18. $25x_0^2 + 121x_1^2 \leq 37$ (resilience index from pansies and verbenas squared)
19. $5x_0 + 11x_1 + 10x_2 + 6x_3 \leq 37$ (total resilience index)
20. $121x_1^2 + 36x_3^2 \leq 23 \times 144$ (verbenas squared plus aloe vera squared)
21. $9x_2 + 7x_3 \leq 28 \times 144$ (potato vines and aloe vera)
22. $2x_0 + 9x_1 + 7x_3 \leq 42 \times 144$ (pansies, verbenas, and aloe vera)
23. $81x_1^2 + 81x_2^2 + 36x_3^2 \leq 46 \times 144$ (verbenas squared, potato vines squared, and aloe vera squared)
24. $4x_0^2 + 81x_1^2 + 81x_2^2 \leq 54 \times 144$ (pansies squared, verbenas squared, and potato vines squared)
25. $4x_0^2 + 81x_1^2 + 81x_2^2 + 36x_3^2 \leq 54 \times 144$ (total)
26. $81x_1^2 + x_2^2 \leq 86$ (verbenas squared and potato vines squared cost)
27. $x_2 + 11x_3 \leq 60$ (potato vines and aloe vera cost)
28. $3x_0 + x_2 \leq 65$ (pansies and potato vines cost)
29. $9x_0^2 + 81x_1^2 + 36x_3^2 \leq 51$ (pansies squared, verbenas squared, and aloe vera squared cost)
30. $9x_1 + x_2 + 11x_3 \leq 59$ (verbenas, potato vines, and aloe vera cost)
31. $3x_0 + 9x_1 + x_2 \leq 67$ (pansies, verbenas, and potato vines cost)
32. $3x_0 + 9x_1 + x_2 + 11x_3 \leq 67$ (total cost)

## 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables and constraints.

```python
import gurobi

# Create a new Gurobi model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="pansies", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="verbenas", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="potato_vines", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="aloe_vera", vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(8*x0**2 + 2*x0*x1 + 2*x0*x2 + x0*x3 + 8*x1**2 + 4*x1*x2 + 8*x1*x3 + 2*x2**2 + x2*x3 + 6*x3**2 + 4*x0 + 2*x1 + 4*x2 + 2*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x0 + 11*x1 + 10*x2 + 6*x3 <= 73)
m.addConstr(2*x0 + 9*x1 + 9*x2 + 7*x3 <= 73)
m.addConstr(3*x0 + 9*x1 + x2 + 11*x3 <= 200)
m.addConstr(2*x0 + 9*x2 >= 17*144)
m.addConstr(9*x1 + 9*x2 >= 17*144)
m.addConstr(2*x0 + 9*x2 + 7*x3 >= 16*144)
m.addConstr(2*x0 + 9*x1 + 7*x3 >= 16*144)
m.addConstr(4*x0**2 + 81*x2**2 + 49*x3**2 >= 10*144)
m.addConstr(2*x0 + 9*x1 + 7*x3 >= 10*144)
m.addConstr(3*x0 + x2 >= 22)
m.addConstr(3*x0 + 9*x1 + x2 >= 35)
m.addConstr(6*x0 - 4*x1 + x2 >= 0)
m.addConstr(10*x2 + 6*x3 <= 28)
m.addConstr(25*x0**2 + 121*x1**2 <= 37)
m.addConstr(5*x0 + 11*x1 + 10*x2 + 6*x3 <= 37)
m.addConstr(121*x1**2 + 36*x3**2 <= 23*144)
m.addConstr(9*x2 + 7*x3 <= 28*144)
m.addConstr(2*x0 + 9*x1 + 7*x3 <= 42*144)
m.addConstr(81*x1**2 + 81*x2**2 + 36*x3**2 <= 46*144)
m.addConstr(4*x0**2 + 81*x1**2 + 81*x2**2 <= 54*144)
m.addConstr(4*x0**2 + 81*x1**2 + 81*x2**2 + 36*x3**2 <= 54*144)
m.addConstr(81*x1**2 + x2**2 <= 86)
m.addConstr(x2 + 11*x3 <= 60)
m.addConstr(3*x0 + x2 <= 65)
m.addConstr(9*x0**2 + 81*x1**2 + 36*x3**2 <= 51)
m.addConstr(9*x1 + x2 + 11*x3 <= 59)
m.addConstr(3*x0 + 9*x1 + x2 <= 67)
m.addConstr(3*x0 + 9*x1 + x2 + 11*x3 <= 67)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("pansies: ", x0.varValue)
    print("verbenas: ", x1.varValue)
    print("potato_vines: ", x2.varValue)
    print("aloe_vera: ", x3.varValue)
else:
    print("No solution found")
```

## Step 5: Symbolic representation
```json
{
    'sym_variables': [('x0', 'pansies'), ('x1', 'verbenas'), ('x2', 'potato vines'), ('x3', 'aloe vera')],
    'objective_function': '8*x0^2 + 2*x0*x1 + 2*x0*x2 + x0*x3 + 8*x1^2 + 4*x1*x2 + 8*x1*x3 + 2*x2^2 + x2*x3 + 6*x3^2 + 4*x0 + 2*x1 + 4*x2 + 2*x3',
    'constraints': [
        '5*x0 + 11*x1 + 10*x2 + 6*x3 <= 73',
        '2*x0 + 9*x1 + 9*x2 + 7*x3 <= 73',
        '3*x0 + 9*x1 + x2 + 11*x3 <= 200',
        '2*x0 + 9*x2 >= 17*144',
        '9*x1 + 9*x2 >= 17*144',
        '2*x0 + 9*x2 + 7*x3 >= 16*144',
        '2*x0 + 9*x1 + 7*x3 >= 16*144',
        '4*x0^2 + 81*x2^2 + 49*x3^2 >= 10*144',
        '2*x0 + 9*x1 + 7*x3 >= 10*144',
        '3*x0 + x2 >= 22',
        '3*x0 + 9*x1 + x2 >= 35',
        '6*x0 - 4*x1 + x2 >= 0',
        '10*x2 + 6*x3 <= 28',
        '25*x0^2 + 121*x1^2 <= 37',
        '5*x0 + 11*x1 + 10*x2 + 6*x3 <= 37',
        '121*x1^2 + 36*x3^2 <= 23*144',
        '9*x2 + 7*x3 <= 28*144',
        '2*x0 + 9*x1 + 7*x3 <= 42*144',
        '81*x1^2 + 81*x2^2 + 36*x3^2 <= 46*144',
        '4*x0^2 + 81*x1^2 + 81*x2^2 <= 54*144',
        '4*x0^2 + 81*x1^2 + 81*x2^2 + 36*x3^2 <= 54*144',
        '81*x1^2 + x2^2 <= 86',
        'x2 + 11*x3 <= 60',
        '3*x0 + x2 <= 65',
        '9*x0^2 + 81*x1^2 + 36*x3^2 <= 51',
        '9*x1 + x2 + 11*x3 <= 59',
        '3*x0 + 9*x1 + x2 <= 67',
        '3*x0 + 9*x1 + x2 + 11*x3 <= 67'
    ]
}
```