## Step 1: Define the symbolic representation of the variables
The variables are 'ham sandwiches', 'corn cobs', 'kiwis', 'chicken thighs' which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $7x_1x_2 + 3x_1x_4 + 5x_2x_3 + 6x_2x_4 + 3x_3^2 + 2x_2 + 3x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $17x_1 + 20x_2 + x_3 + 9x_4 \leq 436$
- $17^2x_1^2 + 20^2x_2^2 \geq 92$
- $20x_2 + x_3 \geq 96$
- $17^2x_1^2 + 9^2x_4^2 \geq 79$
- $17x_1 + 20x_2 + 9x_4 \geq 82$
- $17^2x_1^2 + 20^2x_2^2 + x_3^2 \geq 82$
- $17x_1 + 20x_2 + 9x_4 \geq 90$
- $17x_1 + 20x_2 + x_3 \geq 90$
- $20x_2 + 9x_4 \leq 198$
- $x_3 + 9x_4 \leq 164$
- $17x_1 + 9x_4 \leq 237$
- $17x_1 + 20x_2 + x_3 + 9x_4 \leq 237$

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [
    ('x1', 'ham sandwiches'),
    ('x2', 'corn cobs'),
    ('x3', 'kiwis'),
    ('x4', 'chicken thighs')
],
'objective_function': '7*x1*x2 + 3*x1*x4 + 5*x2*x3 + 6*x2*x4 + 3*x3^2 + 2*x2 + 3*x4',
'constraints': [
    '17*x1 + 20*x2 + x3 + 9*x4 <= 436',
    '17^2*x1^2 + 20^2*x2^2 >= 92',
    '20*x2 + x3 >= 96',
    '17^2*x1^2 + 9^2*x4^2 >= 79',
    '17*x1 + 20*x2 + 9*x4 >= 82',
    '17^2*x1^2 + 20^2*x2^2 + x3^2 >= 82',
    '17*x1 + 20*x2 + 9*x4 >= 90',
    '17*x1 + 20*x2 + x3 >= 90',
    '20*x2 + 9*x4 <= 198',
    'x3 + 9*x4 <= 164',
    '17*x1 + 9*x4 <= 237',
    '17*x1 + 20*x2 + x3 + 9*x4 <= 237'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

# Define the variables
x1 = model.addVar(name="ham_sandwiches", lb=0)
x2 = model.addVar(name="corn_cobs", lb=0)
x3 = model.addVar(name="kiwis", lb=0)
x4 = model.addVar(name="chicken_thighs", lb=0)

# Define the objective function
model.setObjective(7*x1*x2 + 3*x1*x4 + 5*x2*x3 + 6*x2*x4 + 3*x3**2 + 2*x2 + 3*x4, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(17*x1 + 20*x2 + x3 + 9*x4 <= 436)
model.addConstr(17**2*x1**2 + 20**2*x2**2 >= 92)
model.addConstr(20*x2 + x3 >= 96)
model.addConstr(17**2*x1**2 + 9**2*x4**2 >= 79)
model.addConstr(17*x1 + 20*x2 + 9*x4 >= 82)
model.addConstr(17**2*x1**2 + 20**2*x2**2 + x3**2 >= 82)
model.addConstr(17*x1 + 20*x2 + 9*x4 >= 90)
model.addConstr(17*x1 + 20*x2 + x3 >= 90)
model.addConstr(20*x2 + 9*x4 <= 198)
model.addConstr(x3 + 9*x4 <= 164)
model.addConstr(17*x1 + 9*x4 <= 237)
model.addConstr(17*x1 + 20*x2 + x3 + 9*x4 <= 237)

# Update the model
model.update()

# Solve the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Ham sandwiches: ", x1.x)
    print("Corn cobs: ", x2.x)
    print("Kiwis: ", x3.x)
    print("Chicken thighs: ", x4.x)
else:
    print("The model is infeasible")
```