## Step 1: Define the symbolic representation of the variables
The variables are ['chicken breasts', 'rotisserie chickens', 'cantaloupes', 'potatoes'] which can be represented symbolically as ['x0', 'x1', 'x2', 'x3'].

## Step 2: Create a symbolic representation of the problem
The symbolic representation of the variables is:
- x0: chicken breasts
- x1: rotisserie chickens
- x2: cantaloupes
- x3: potatoes

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is: $3x0^2 + 6x0x1 + 7x0x2 + 9x0x3 + 5x1^2 + x1x2 + 5x2^2 + 8x2x3 + 6x0 + 5x1 + 3x2 + 8x3$.

## 4: List the constraints in symbolic notation
The constraints are:
- $20x0 \leq 109$ (cost of chicken breasts)
- $9x0 \leq 173$ (iron from chicken breasts)
- $14x1 \leq 109$ (cost of rotisserie chickens)
- $21x1 \leq 173$ (iron from rotisserie chickens)
- $4x2 \leq 109$ (cost of cantaloupes)
- $9x2 \leq 173$ (iron from cantaloupes)
- $19x3 \leq 109$ (cost of potatoes)
- $21x3 \leq 173$ (iron from potatoes)
- $14x1 + 19x3 \geq 18$ is not correct, $x1^2 + x2^2 + x3^2 \geq 18$ 
- $x0^2 + x2^2 + x3^2 \geq 18$
- $14x1 + 4x2 + 19x3 \geq 25$ is not correct, $14x1 + 4x2 + 19x3 \geq 25$ is correct as is.
- $20x0 + 4x2 + 19x3 \geq 25$
- $21x1 + 21x3 \geq 14$ is not correct, $21x1 + 9x0 + 21x3 \geq 14$ is not correct, $21x1 + 21x3 \geq 14$ 
- $9x2 + 21x3 \geq 19$
- $9x0^2 + 21x1^2 + 9x2^2 \geq 27$
- $9x0 + 21x1 + 21x3 \geq 27$
- $9x0 + 21x1 + 9x2 \geq 23$
- $9x0 + 21x1 + 21x3 \geq 23$
- $4x2 + 19x3 \leq 90$
- $20x0 + 14x1 \leq 43$
- $20x0 + 14x1 + 4x2 + 19x3 \leq 43$
- $9x0 + 21x1 \leq 173$
- $9x0 + 21x1 + 9x2 + 21x3 \leq 173$

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

# Define the model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="chicken_breasts", lb=0)
x1 = m.addVar(name="rotisserie_chickens", lb=0)
x2 = m.addVar(name="cantaloupes", lb=0)
x3 = m.addVar(name="potatoes", lb=0)

# Define the objective function
m.setObjective(3*x0**2 + 6*x0*x1 + 7*x0*x2 + 9*x0*x3 + 5*x1**2 + x1*x2 + 5*x2**2 + 8*x2*x3 + 6*x0 + 5*x1 + 3*x2 + 8*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x0 <= 109)
m.addConstr(9*x0 <= 173)
m.addConstr(14*x1 <= 109)
m.addConstr(21*x1 <= 173)
m.addConstr(4*x2 <= 109)
m.addConstr(9*x2 <= 173)
m.addConstr(19*x3 <= 109)
m.addConstr(21*x3 <= 173)
m.addConstr(x1**2 + x2**2 + x3**2 >= 18)
m.addConstr(x0**2 + x2**2 + x3**2 >= 18)
m.addConstr(14*x1 + 4*x2 + 19*x3 >= 25)
m.addConstr(20*x0 + 4*x2 + 19*x3 >= 25)
m.addConstr(21*x1 + 21*x3 >= 14)
m.addConstr(9*x2 + 21*x3 >= 19)
m.addConstr(9*x0**2 + 21*x1**2 + 9*x2**2 >= 27)
m.addConstr(9*x0 + 21*x1 + 21*x3 >= 27)
m.addConstr(9*x0 + 21*x1 + 9*x2 >= 23)
m.addConstr(9*x0 + 21*x1 + 21*x3 >= 23)
m.addConstr(4*x2 + 19*x3 <= 90)
m.addConstr(20*x0 + 14*x1 <= 43)
m.addConstr(20*x0 + 14*x1 + 4*x2 + 19*x3 <= 43)
m.addConstr(9*x0 + 21*x1 <= 173)
m.addConstr(9*x0 + 21*x1 + 9*x2 + 21*x3 <= 173)

# Optimize the model
m.optimize()

# Print the solution
print("Objective: ", m.objVal)
print("Chicken Breasts: ", x0.varValue)
print("Rotisserie Chickens: ", x1.varValue)
print("Cantaloupes: ", x2.varValue)
print("Potatoes: ", x3.varValue)

```
## Step 6: Create the symbolic representation in JSON
```json
{
    "sym_variables": [
        ["x0", "chicken breasts"],
        ["x1", "rotisserie chickens"],
        ["x2", "cantaloupes"],
        ["x3", "potatoes"]
    ],
    "objective_function": "3*x0^2 + 6*x0*x1 + 7*x0*x2 + 9*x0*x3 + 5*x1^2 + x1*x2 + 5*x2^2 + 8*x2*x3 + 6*x0 + 5*x1 + 3*x2 + 8*x3",
    "constraints": [
        "20*x0 <= 109",
        "9*x0 <= 173",
        "14*x1 <= 109",
        "21*x1 <= 173",
        "4*x2 <= 109",
        "9*x2 <= 173",
        "19*x3 <= 109",
        "21*x3 <= 173",
        "x1^2 + x2^2 + x3^2 >= 18",
        "x0^2 + x2^2 + x3^2 >= 18",
        "14*x1 + 4*x2 + 19*x3 >= 25",
        "20*x0 + 4*x2 + 19*x3 >= 25",
        "21*x1 + 21*x3 >= 14",
        "9*x2 + 21*x3 >= 19",
        "9*x0^2 + 21*x1^2 + 9*x2^2 >= 27",
        "9*x0 + 21*x1 + 21*x3 >= 27",
        "9*x0 + 21*x1 + 9*x2 >= 23",
        "9*x0 + 21*x1 + 21*x3 >= 23",
        "4*x2 + 19*x3 <= 90",
        "20*x0 + 14*x1 <= 43",
        "20*x0 + 14*x1 + 4*x2 + 19*x3 <= 43",
        "9*x0 + 21*x1 <= 173",
        "9*x0 + 21*x1 + 9*x2 + 21*x3 <= 173"
    ]
}
```