## Step 1: Define the symbolic representation of the variables
The variables are 'bowls of instant ramen', 'steaks', 'peanutbutter sandwiches', and 'granola bars', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $3.62x_0^2 + 4.63x_0x_1 + 5.03x_0x_3 + 2.07x_1^2 + 6.03x_1x_2 + 3.6x_1x_3 + 6.97x_2^2 + 7.45x_2x_3 + 4.02x_3^2 + 9.15x_0 + 9.81x_1 + 8.4x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
- $3.51x_0 \leq 139$
- $1.79x_0 \leq 203$
- $7.74x_0 \leq 161$
- $0.65x_1 \leq 139$
- $5.28x_1 \leq 203$
- $7.25x_1 \leq 161$
- $8.37x_2 \leq 139$
- $7.08x_2 \leq 203$
- $6.01x_2 \leq 161$
- $1.67x_3 \leq 139$
- $7.75x_3 \leq 203$
- $7.62x_3 \leq 161$
- $7.74x_0 + 6.01x_2 \geq 29$
- $(8.37x_2)^2 + (1.67x_3)^2 \leq 44$
- $3.51x_0 + 0.65x_1 \leq 59$
- $3.51x_0 + 8.37x_2 \leq 104$
- $(0.65x_1)^2 + (1.67x_3)^2 \leq 95$
- $3.51x_0 + 0.65x_1 + 8.37x_2 \leq 65$
- $3.51x_0 + 0.65x_1 + 8.37x_2 + 1.67x_3 \leq 65$
- $(5.28x_1)^2 + (7.08x_2)^2 \leq 59$
- $1.79x_0 + 7.08x_2 \leq 56$
- $1.79x_0 + 5.28x_1 \leq 109$
- $(5.28x_1)^2 + (7.75x_3)^2 \leq 85$
- $1.79x_0 + 5.28x_1 + 7.08x_2 + 7.75x_3 \leq 85$
- $7.74x_0 + 6.01x_2 \leq 140$
- $(7.74x_0)^2 + (7.62x_3)^2 \leq 56$
- $7.25x_1 + 6.01x_2 \leq 105$
- $7.74x_0 + 7.25x_1 + 6.01x_2 + 7.62x_3 \leq 105$

## 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'bowls of instant ramen'),
        ('x1', 'steaks'),
        ('x2', 'peanutbutter sandwiches'),
        ('x3', 'granola bars')
    ],
    'objective_function': '3.62x0^2 + 4.63x0*x1 + 5.03x0*x3 + 2.07x1^2 + 6.03x1*x2 + 3.6x1*x3 + 6.97x2^2 + 7.45x2*x3 + 4.02x3^2 + 9.15x0 + 9.81x1 + 8.4x3',
    'constraints': [
        '3.51x0 <= 139',
        '1.79x0 <= 203',
        '7.74x0 <= 161',
        '0.65x1 <= 139',
        '5.28x1 <= 203',
        '7.25x1 <= 161',
        '8.37x2 <= 139',
        '7.08x2 <= 203',
        '6.01x2 <= 161',
        '1.67x3 <= 139',
        '7.75x3 <= 203',
        '7.62x3 <= 161',
        '7.74x0 + 6.01x2 >= 29',
        '(8.37x2)^2 + (1.67x3)^2 <= 44',
        '3.51x0 + 0.65x1 <= 59',
        '3.51x0 + 8.37x2 <= 104',
        '(0.65x1)^2 + (1.67x3)^2 <= 95',
        '3.51x0 + 0.65x1 + 8.37x2 <= 65',
        '3.51x0 + 0.65x1 + 8.37x2 + 1.67x3 <= 65',
        '(5.28x1)^2 + (7.08x2)^2 <= 59',
        '1.79x0 + 7.08x2 <= 56',
        '1.79x0 + 5.28x1 <= 109',
        '(5.28x1)^2 + (7.75x3)^2 <= 85',
        '1.79x0 + 5.28x1 + 7.08x2 + 7.75x3 <= 85',
        '7.74x0 + 6.01x2 <= 140',
        '(7.74x0)^2 + (7.62x3)^2 <= 56',
        '7.25x1 + 6.01x2 <= 105',
        '7.74x0 + 7.25x1 + 6.01x2 + 7.62x3 <= 105'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # bowls of instant ramen
x1 = m.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # steaks
x2 = m.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # peanutbutter sandwiches
x3 = m.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # granola bars

# Objective function
m.setObjective(3.62*x0**2 + 4.63*x0*x1 + 5.03*x0*x3 + 2.07*x1**2 + 6.03*x1*x2 + 3.6*x1*x3 + 6.97*x2**2 + 7.45*x2*x3 + 4.02*x3**2 + 9.15*x0 + 9.81*x1 + 8.4*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(3.51*x0 <= 139)
m.addConstr(1.79*x0 <= 203)
m.addConstr(7.74*x0 <= 161)
m.addConstr(0.65*x1 <= 139)
m.addConstr(5.28*x1 <= 203)
m.addConstr(7.25*x1 <= 161)
m.addConstr(8.37*x2 <= 139)
m.addConstr(7.08*x2 <= 203)
m.addConstr(6.01*x2 <= 161)
m.addConstr(1.67*x3 <= 139)
m.addConstr(7.75*x3 <= 203)
m.addConstr(7.62*x3 <= 161)
m.addConstr(7.74*x0 + 6.01*x2 >= 29)
m.addConstr((8.37*x2)**2 + (1.67*x3)**2 <= 44)
m.addConstr(3.51*x0 + 0.65*x1 <= 59)
m.addConstr(3.51*x0 + 8.37*x2 <= 104)
m.addConstr((0.65*x1)**2 + (1.67*x3)**2 <= 95)
m.addConstr(3.51*x0 + 0.65*x1 + 8.37*x2 <= 65)
m.addConstr(3.51*x0 + 0.65*x1 + 8.37*x2 + 1.67*x3 <= 65)
m.addConstr((5.28*x1)**2 + (7.08*x2)**2 <= 59)
m.addConstr(1.79*x0 + 7.08*x2 <= 56)
m.addConstr(1.79*x0 + 5.28*x1 <= 109)
m.addConstr((5.28*x1)**2 + (7.75*x3)**2 <= 85)
m.addConstr(1.79*x0 + 5.28*x1 + 7.08*x2 + 7.75*x3 <= 85)
m.addConstr(7.74*x0 + 6.01*x2 <= 140)
m.addConstr((7.74*x0)**2 + (7.62*x3)**2 <= 56)
m.addConstr(7.25*x1 + 6.01*x2 <= 105)
m.addConstr(7.74*x0 + 7.25*x1 + 6.01*x2 + 7.62*x3 <= 105)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("bowls of instant ramen: ", x0.varValue)
    print("steaks: ", x1.varValue)
    print("peanutbutter sandwiches: ", x2.varValue)
    print("granola bars: ", x3.varValue)
else:
    print("The model is infeasible")
```