## Step 1: Define the symbolic representation of the variables
The variables are 'peanutbutter sandwiches', 'pickles', 'bowls of cereal', and 'ravioli', 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: $1 \cdot x_1^2 + 3 \cdot x_1 \cdot x_2 + 3 \cdot x_1 \cdot x_3 + 1 \cdot x_1 \cdot x_4 + 9 \cdot x_2^2 + 8 \cdot x_3 \cdot x_4 + 4 \cdot x_4^2 + 8 \cdot x_1 + 6 \cdot x_3 + 5 \cdot x_4$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $0.91x_1 + 0.63x_2 + 1.79x_3 + 0.71x_4 \leq 162$ (total carbohydrates constraint)
2. $0.63x_2 + 0.71x_4 \geq 26$ (carbohydrates from pickles and ravioli)
3. $0.91^2x_1^2 + 1.79^2x_3^2 \leq 112$ (carbohydrates from peanutbutter sandwiches and bowls of cereal squared)
4. $0.63x_2 + 1.79x_3 \leq 63$ (carbohydrates from pickles and bowls of cereal)
5. $0.63x_2 + 0.71x_4 \leq 69$ (carbohydrates from pickles and ravioli)
6. $0.63x_2 + 1.79x_3 + 0.71x_4 \leq 138$ (carbohydrates from pickles, bowls of cereal, and ravioli)
7. $0.91x_1 + 0.63x_2 + 0.71x_4 \leq 126$ (carbohydrates from peanutbutter sandwiches, pickles, and ravioli)
8. $0.91x_1 + 0.63x_2 + 1.79x_3 \leq 44$ (carbohydrates from peanutbutter sandwiches, pickles, and bowls of cereal)
9. $0.91x_1 + 0.63x_2 + 1.79x_3 + 0.71x_4 \leq 44$ (carbohydrates from all sources)

## 4: Create a symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'peanutbutter sandwiches'),
        ('x2', 'pickles'),
        ('x3', 'bowls of cereal'),
        ('x4', 'ravioli')
    ],
    'objective_function': '1*x1^2 + 3*x1*x2 + 3*x1*x3 + 1*x1*x4 + 9*x2^2 + 8*x3*x4 + 4*x4^2 + 8*x1 + 6*x3 + 5*x4',
    'constraints': [
        '0.91*x1 + 0.63*x2 + 1.79*x3 + 0.71*x4 <= 162',
        '0.63*x2 + 0.71*x4 >= 26',
        '0.91^2*x1^2 + 1.79^2*x3^2 <= 112',
        '0.63*x2 + 1.79*x3 <= 63',
        '0.63*x2 + 0.71*x4 <= 69',
        '0.63*x2 + 1.79*x3 + 0.71*x4 <= 138',
        '0.91*x1 + 0.63*x2 + 0.71*x4 <= 126',
        '0.91*x1 + 0.63*x2 + 1.79*x3 <= 44',
        '0.91*x1 + 0.63*x2 + 1.79*x3 + 0.71*x4 <= 44'
    ]
}
```

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

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

# Define the variables
x1 = m.addVar(name="peanutbutter_sandwiches", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = m.addVar(name="pickles", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x3 = m.addVar(name="bowls_of_cereal", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x4 = m.addVar(name="ravioli", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Define the objective function
m.setObjective(1*x1**2 + 3*x1*x2 + 3*x1*x3 + x1*x4 + 9*x2**2 + 8*x3*x4 + 4*x4**2 + 8*x1 + 6*x3 + 5*x4, gurobi.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(0.91*x1 + 0.63*x2 + 1.79*x3 + 0.71*x4 <= 162)
m.addConstr(0.63*x2 + 0.71*x4 >= 26)
m.addConstr(0.91**2*x1**2 + 1.79**2*x3**2 <= 112)
m.addConstr(0.63*x2 + 1.79*x3 <= 63)
m.addConstr(0.63*x2 + 0.71*x4 <= 69)
m.addConstr(0.63*x2 + 1.79*x3 + 0.71*x4 <= 138)
m.addConstr(0.91*x1 + 0.63*x2 + 0.71*x4 <= 126)
m.addConstr(0.91*x1 + 0.63*x2 + 1.79*x3 <= 44)
m.addConstr(0.91*x1 + 0.63*x2 + 1.79*x3 + 0.71*x4 <= 44)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.Status.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Peanutbutter sandwiches: ", x1.varValue)
    print("Pickles: ", x2.varValue)
    print("Bowls of cereal: ", x3.varValue)
    print("Ravioli: ", x4.varValue)
else:
    print("The model is infeasible")
```