## Step 1: Define the variables and their corresponding symbolic notation
Let's denote the variables as follows:
- $x_1$ = rotisserie chickens
- $x_2$ = hot dogs
- $x_3$ = bowls of cereal
- $x_4$ = potatoes
- $x_5$ = ham sandwiches

## Step 2: Formulate the objective function
The objective function to maximize is:
$8.85x_1^2 + 3.16x_1x_2 + 5.35x_1x_3 + 3.6x_1x_4 + 4.1x_1x_5 + 5.18x_2^2 + 3.79x_2x_3 + 9.68x_2x_4 + 5.14x_2x_5 + 5.98x_3^2 + 1.65x_3x_4 + 1.24x_3x_5 + 6.41x_4^2 + 9.39x_4x_5 + 7.18x_5^2 + 7.88x_1 + 6.53x_2 + 2.05x_3 + 6.31x_4 + 1.62x_5$

## 3: Define the constraints
Constraints:
1. $11x_1 + 2x_2 + 10x_3 + x_4 + 7x_5 \leq 100$
2. $10x_3 + 7x_5 \geq 7$
3. $2x_2 + x_4 \geq 10$
4. $11x_1 + 2x_2 \geq 19$
5. $11x_1 + 7x_5 \geq 18$
6. $11x_1 + 2x_2 + 10x_3 \geq 12$
7. $11^2x_1^2 + 10^2x_3^2 + 7^2x_5^2 \geq 12$
8. $2x_2 + x_4 + 7x_5 \geq 12$
9. $2x_2 + 10x_3 + 7x_5 \geq 12$
10. $11x_1 + 2x_2 + 7x_5 \geq 12$
11. $11x_1 + 2x_2 + 10x_3 \geq 16$
12. $11x_1 + 10x_3 + 7x_5 \geq 16$
13. $2x_2 + x_4 + 7x_5 \geq 16$
14. $2x_2 + 10x_3 + 7x_5 \geq 16$
15. $11^2x_1^2 + 2^2x_2^2 + 7^2x_5^2 \geq 16$
16. $11x_1 + 2x_2 + 10x_3 \geq 17$
17. $11^2x_1^2 + 10^2x_3^2 + 7^2x_5^2 \geq 17$
18. $2x_2 + x_4 + 7x_5 \geq 17$
19. $2^2x_2^2 + 10^2x_3^2 + 7^2x_5^2 \geq 17$
20. $11^2x_1^2 + 2^2x_2^2 + 7^2x_5^2 \geq 17$
21. $11x_1 + 2x_2 + 10x_3 \geq 15$
22. $11x_1 + 10x_3 + 7x_5 \geq 15$
23. $2^2x_2^2 + x_4^2 + 7^2x_5^2 \geq 15$
24. $2x_2 + 10x_3 + 7x_5 \geq 15$
25. $11x_1 + 2x_2 + 7x_5 \geq 15$
26. $11x_1 + 2x_2 + 10x_3 \geq 16$
27. $11x_1 + 10x_3 + 7x_5 \geq 16$
28. $2x_2 + x_4 + 7x_5 \geq 16$
29. $2x_2 + 10x_3 + 7x_5 \geq 16$
30. $11x_1 + 2x_2 + 7x_5 \geq 16$
31. $10x_3 + x_4 \leq 45$
32. $11x_1 + 7x_5 \leq 51$
33. $2x_2 + x_4 \leq 74$
34. $11^2x_1^2 + x_4^2 \leq 94$
35. $11^2x_1^2 + 10^2x_3^2 \leq 32$
36. $x_4 + 7x_5 \leq 86$
37. $2^2x_2^2 + 10^2x_3^2 \leq 96$
38. $2^2x_2^2 + 7^2x_5^2 \leq 24$
39. $11x_1 + 2x_2 + 10x_3 + x_4 + 7x_5 \leq 24$

## 4: Specify variable bounds and types
- $x_1$ is continuous
- $x_2$ is integer
- $x_3$ is continuous
- $x_4$ is continuous
- $x_5$ is integer

## 5: Convert to Gurobi code
```python
import gurobi as gp

# Define variables
x1 = gp.Var(name="rotisserie_chickens", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x2 = gp.Var(name="hot_dogs", lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER)
x3 = gp.Var(name="bowls_of_cereal", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x4 = gp.Var(name="potatoes", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x5 = gp.Var(name="ham_sandwiches", lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER)

# Create model
m = gp.Model()

# Objective function
m.setObjective(8.85*x1**2 + 3.16*x1*x2 + 5.35*x1*x3 + 3.6*x1*x4 + 4.1*x1*x5 + 
               5.18*x2**2 + 3.79*x2*x3 + 9.68*x2*x4 + 5.14*x2*x5 + 5.98*x3**2 + 
               1.65*x3*x4 + 1.24*x3*x5 + 6.41*x4**2 + 9.39*x4*x5 + 7.18*x5**2 + 
               7.88*x1 + 6.53*x2 + 2.05*x3 + 6.31*x4 + 1.62*x5, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(11*x1 + 2*x2 + 10*x3 + x4 + 7*x5 <= 100)
m.addConstr(10*x3 + 7*x5 >= 7)
m.addConstr(2*x2 + x4 >= 10)
m.addConstr(11*x1 + 2*x2 >= 19)
m.addConstr(11*x1 + 7*x5 >= 18)
m.addConstr(11*x1 + 2*x2 + 10*x3 >= 12)
m.addConstr(11**2*x1**2 + 10**2*x3**2 + 7**2*x5**2 >= 12)
m.addConstr(2*x2 + x4 + 7*x5 >= 12)
m.addConstr(2*x2 + 10*x3 + 7*x5 >= 12)
m.addConstr(11*x1 + 2*x2 + 7*x5 >= 12)
m.addConstr(11*x1 + 2*x2 + 10*x3 >= 16)
m.addConstr(11*x1 + 10*x3 + 7*x5 >= 16)
m.addConstr(2*x2 + x4 + 7*x5 >= 16)
m.addConstr(2*x2 + 10*x3 + 7*x5 >= 16)
m.addConstr(11**2*x1**2 + 2**2*x2**2 + 7**2*x5**2 >= 16)
m.addConstr(11*x1 + 2*x2 + 10*x3 >= 17)
m.addConstr(11**2*x1**2 + 10**2*x3**2 + 7**2*x5**2 >= 17)
m.addConstr(2*x2 + x4 + 7*x5 >= 17)
m.addConstr(2**2*x2**2 + 10**2*x3**2 + 7**2*x5**2 >= 17)
m.addConstr(11**2*x1**2 + 2**2*x2**2 + 7**2*x5**2 >= 17)
m.addConstr(11*x1 + 2*x2 + 10*x3 >= 15)
m.addConstr(11*x1 + 10*x3 + 7*x5 >= 15)
m.addConstr(2**2*x2**2 + x4**2 + 7**2*x5**2 >= 15)
m.addConstr(2*x2 + 10*x3 + 7*x5 >= 15)
m.addConstr(11*x1 + 2*x2 + 7*x5 >= 15)
m.addConstr(11*x1 + 2*x2 + 10*x3 >= 16)
m.addConstr(11*x1 + 10*x3 + 7*x5 >= 16)
m.addConstr(2*x2 + x4 + 7*x5 >= 16)
m.addConstr(2*x2 + 10*x3 + 7*x5 >= 16)
m.addConstr(11*x1 + 2*x2 + 7*x5 >= 16)
m.addConstr(10*x3 + x4 <= 45)
m.addConstr(11*x1 + 7*x5 <= 51)
m.addConstr(2*x2 + x4 <= 74)
m.addConstr(11**2*x1**2 + x4**2 <= 94)
m.addConstr(11**2*x1**2 + 10**2*x3**2 <= 32)
m.addConstr(x4 + 7*x5 <= 86)
m.addConstr(2**2*x2**2 + 10**2*x3**2 <= 96)
m.addConstr(2**2*x2**2 + 7**2*x5**2 <= 24)
m.addConstr(11*x1 + 2*x2 + 10*x3 + x4 + 7*x5 <= 24)

# Solve model
m.optimize()

# Print solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
    print("x4: ", x4.varValue)
    print("x5: ", x5.varValue)
else:
    print("No solution found")
```

## Step 6: Symbolic representation
```json
{
    'sym_variables': [
        ('x1', 'rotisserie chickens'), 
        ('x2', 'hot dogs'), 
        ('x3', 'bowls of cereal'), 
        ('x4', 'potatoes'), 
        ('x5', 'ham sandwiches')
    ], 
    'objective_function': '8.85*x1^2 + 3.16*x1*x2 + 5.35*x1*x3 + 3.6*x1*x4 + 4.1*x1*x5 + 5.18*x2^2 + 3.79*x2*x3 + 9.68*x2*x4 + 5.14*x2*x5 + 5.98*x3^2 + 1.65*x3*x4 + 1.24*x3*x5 + 6.41*x4^2 + 9.39*x4*x5 + 7.18*x5^2 + 7.88*x1 + 6.53*x2 + 2.05*x3 + 6.31*x4 + 1.62*x5', 
    'constraints': [
        '11*x1 + 2*x2 + 10*x3 + x4 + 7*x5 <= 100',
        '10*x3 + 7*x5 >= 7',
        '2*x2 + x4 >= 10',
        '11*x1 + 2*x2 >= 19',
        '11*x1 + 7*x5 >= 18',
        '11*x1 + 2*x2 + 10*x3 >= 12',
        '121*x1^2 + 100*x3^2 + 49*x5^2 >= 12',
        '2*x2 + x4 + 7*x5 >= 12',
        '2*x2 + 10*x3 + 7*x5 >= 12',
        '11*x1 + 2*x2 + 7*x5 >= 12',
        '11*x1 + 2*x2 + 10*x3 >= 16',
        '11*x1 + 10*x3 + 7*x5 >= 16',
        '2*x2 + x4 + 7*x5 >= 16',
        '2*x2 + 10*x3 + 7*x5 >= 16',
        '121*x1^2 + 4*x2^2 + 49*x5^2 >= 16',
        '11*x1 + 2*x2 + 10*x3 >= 17',
        '121*x1^2 + 100*x3^2 + 49*x5^2 >= 17',
        '2*x2 + x4 + 7*x5 >= 17',
        '4*x2^2 + 100*x3^2 + 49*x5^2 >= 17',
        '121*x1^2 + 4*x2^2 + 49*x5^2 >= 17',
        '11*x1 + 2*x2 + 10*x3 >= 15',
        '11*x1 + 10*x3 + 7*x5 >= 15',
        '4*x2^2 + x4^2 + 49*x5^2 >= 15',
        '2*x2 + 10*x3 + 7*x5 >= 15',
        '11*x1 + 2*x2 + 7*x5 >= 15',
        '11*x1 + 2*x2 + 10*x3 >= 16',
        '11*x1 + 10*x3 + 7*x5 >= 16',
        '2*x2 + x4 + 7*x5 >= 16',
        '2*x2 + 10*x3 + 7*x5 >= 16',
        '11*x1 + 2*x2 + 7*x5 >= 16',
        '10*x3 + x4 <= 45',
        '11*x1 + 7*x5 <= 51',
        '2*x2 + x4 <= 74',
        '121*x1^2 + x4^2 <= 94',
        '121*x1^2 + 100*x3^2 <= 32',
        'x4 + 7*x5 <= 86',
        '4*x2^2 + 100*x3^2 <= 96',
        '4*x2^2 + 49*x5^2 <= 24',
        '11*x1 + 2*x2 + 10*x3 + x4 + 7*x5 <= 24'
    ]
}
```