## Step 1: Define the symbolic representation of the variables
The variables are 'knishes', 'blueberry pies', and 'ham sandwiches', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $3.9x_0^2 + 2.38x_0x_1 + 3.84x_0x_2 + 1.0x_1^2 + 6.7x_1x_2 + 5.99x_2^2 + 7.68x_0 + 6.25x_1 + 2.01x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $35x_0 + 10x_1 + 17x_2 \leq 491$ (grams of fat)
- $5x_0 + 31x_1 + 5x_2 \leq 377$ (umami index)
- $10x_0 + 22x_1 + 20x_2 \leq 251$ (dollar cost)
- $10x_1 + 17x_2 \geq 132$ (minimum grams of fat from blueberry pies and ham sandwiches)
- $10x_0 + 22x_1 \geq 41$ (minimum spend on knishes and blueberry pies)
- $8x_1^2 - 9x_2^2 \geq 0$
- $35x_0 + 10x_1 \leq 312$ (maximum grams of fat from knishes and blueberry pies)
- $10x_1^2 + 17x_2^2 \leq 304$ (maximum grams of fat from blueberry pies squared and ham sandwiches squared)
- $35x_0 + 10x_1 + 17x_2 \leq 304$ (alternative representation, but seems redundant with the first fat constraint)
- $5x_0 + 5x_2 \leq 176$ (umami index from knishes and ham sandwiches)
- $5x_0 + 31x_1 + 5x_2 \leq 141$ (total umami index)
- $22x_1^2 + 20x_2^2 \leq 89$ (maximum spend on blueberry pies squared and ham sandwiches squared)
- $10x_0 + 22x_1 \leq 215$ (maximum spend on knishes and blueberry pies)
- $10x_0 + 22x_1 + 20x_2 \leq 215$ (maximum spend on knishes, blueberry pies, and ham sandwiches)

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'knishes'), ('x1', 'blueberry pies'), ('x2', 'ham sandwiches')],
'objective_function': '3.9x0^2 + 2.38x0x1 + 3.84x0x2 + 1.0x1^2 + 6.7x1x2 + 5.99x2^2 + 7.68x0 + 6.25x1 + 2.01x2',
'constraints': [
'35x0 + 10x1 + 17x2 <= 491',
'5x0 + 31x1 + 5x2 <= 377',
'10x0 + 22x1 + 20x2 <= 251',
'10x1 + 17x2 >= 132',
'10x0 + 22x1 >= 41',
'8x1^2 - 9x2^2 >= 0',
'35x0 + 10x1 <= 312',
'10x1^2 + 17x2^2 <= 304',
'35x0 + 10x1 + 17x2 <= 304',
'5x0 + 5x2 <= 176',
'5x0 + 31x1 + 5x2 <= 141',
'22x1^2 + 20x2^2 <= 89',
'10x0 + 22x1 <= 215',
'10x0 + 22x1 + 20x2 <= 215'
]
}
```

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

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="knishes", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x1 = model.addVar(name="blueberry_pies", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = model.addVar(name="ham_sandwiches", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Define the objective function
model.setObjective(3.9*x0**2 + 2.38*x0*x1 + 3.84*x0*x2 + 1.0*x1**2 + 6.7*x1*x2 + 5.99*x2**2 + 7.68*x0 + 6.25*x1 + 2.01*x2, gurobi.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(35*x0 + 10*x1 + 17*x2 <= 491)
model.addConstr(5*x0 + 31*x1 + 5*x2 <= 377)
model.addConstr(10*x0 + 22*x1 + 20*x2 <= 251)
model.addConstr(10*x1 + 17*x2 >= 132)
model.addConstr(10*x0 + 22*x1 >= 41)
model.addConstr(8*x1**2 - 9*x2**2 >= 0)
model.addConstr(35*x0 + 10*x1 <= 312)
model.addConstr(10*x1**2 + 17*x2**2 <= 304)
model.addConstr(35*x0 + 10*x1 + 17*x2 <= 304)
model.addConstr(5*x0 + 5*x2 <= 176)
model.addConstr(5*x0 + 31*x1 + 5*x2 <= 141)
model.addConstr(22*x1**2 + 20*x2**2 <= 89)
model.addConstr(10*x0 + 22*x1 <= 215)
model.addConstr(10*x0 + 22*x1 + 20*x2 <= 215)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Knishes: ", x0.varValue)
    print("Blueberry Pies: ", x1.varValue)
    print("Ham Sandwiches: ", x2.varValue)
else:
    print("The model is infeasible")
```